TEST BANK for Essentials of Health Policy and Law 4th Edition by Joel Teitelbaum and Sara Wilensky.

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Chapter: Chapter 01 - Quiz

Multiple Choice

1. A subset of the population of interest is often referred to by what statistical term?

A) A sample of individuals B) A subculture of individuals C) A class of individuals D) A minority group Ans: A Complexity: Easy Ahead: What is Biostatistics?

Subject: Chapter 1

2. The measure of uncertainty in a biostatistician’s calculation of a particular outcome that may result from using a subset of the population to estimate the actual likelihood of the event occurring in the population as a whole is referred to by what statistical term?

A) A chance error B) A systematic error C) A standard error D) A margin of error Ans: D Complexity: Easy Ahead: How Is the Extent of Disease in a Group or Region Quantified?

Subject: Chapter 1

3. Which of the following most appropriately describes how the data from a cross-sectional study can be applied to a population?

A) The data generated from a cross-sectional study can be applied to new or changing populations regardless of the amount of time that has passed since the study was conducted.

B) The data generated from a cross-sectional study is only applicable to the original population of interest during the time that the study was conducted.

C) The data generated from a cross-sectional study is applicable to any group of individuals with similar characteristics to the original population of interest.

D) The data generated from a cross-sectional study is applicable to all individuals regardless of how much those individuals differ from the original population of interest.

Ans: B Complexity: Moderate Ahead: How Is the Extent of Disease in a Group or Region Quantified?

Subject: Chapter 1

4. Researchers have conducted a study and determined that the relative risk for developing a cold for individuals taking vitamin C is 0.47 when compared to the number of participants in the study who developed a cold while not taking vitamin C. This is an indication of which of the following?

A) This indicates that people who took vitamin C were 47% more likely to catch a cold and that taking vitamin C makes people more susceptible to catching a cold.

B) This indicates that the individuals taking vitamin C were 47% less likely to catch a cold and that taking vitamin C has a protective effect, making them less likely to catch a cold.

C) This indicates that the individuals taking vitamin C were 53% less likely to catch a cold and that taking vitamin C has a protective effect, making them less likely to catch a cold.

D) Only relative risk ratios above one are statistically significant, a relative risk ratio below one indicates there is no difference between the individuals who take vitamin C and those individuals who do not.

Ans: C Complexity: Difficult Ahead: How Are Risk Factors or Characteristics That Might Be Related to the Development or Progression of Disease Identified?

Subject: Chapter 1

5. Which is the most important factor in determining which populations a well-designed study’s results can be applied to?

A) The inclusion and exclusion criteria for the study B) The randomization of participants for a study C) The type of study being conducted D) The presence of blinding throughout the study Ans: A Complexity: Difficult Ahead: How Is the Effectiveness of a New Drug Determined?

Subject: Chapter 1

True/False

1. True or False? Biostatistics is defined as the application of statistical principles in medicine, public health, or biology.

Ans: True Complexity: Easy Ahead: What Is Biostatistics?

Subject: Chapter 1

2. True or False? The data collected in a biostatistics study can be applied to any population regardless of race, class, and socioeconomic status.

Ans: False Complexity: Easy Ahead: What Are the Issues?

Subject: Chapter 1

3. True or False? A relative risk of 5.67 indicates that the group of individuals in a study exposed to the particular variable of interest are 5.67 times more likely to experience the observed outcome being studied.

Ans: True Complexity: Moderate Ahead: How Are Risk Factors or Characteristics That Might Be Related to the Development or Progression of Disease Identified?

Subject: Chapter 1

4. True or False? Oftentimes it is more difficult to establish a relationship between a particular disease outcome and a risk factor among older adults because they also have other risk factors for disease.

Ans: True Complexity: Moderate Ahead: How Are Risk Factors or Characteristics That Might Be Related to the Development or Progression of Disease Identified?

Subject: Chapter 1

5. True or False? Randomization of clinical trial participants is important to ensure that clinical trial participants in the treatment group and comparator group allow the study’s results to be generalized to the population as a whole, and not just the subgroup of individuals that participated in the study because of the balance promoted through the randomization process.

Ans: False Complexity: Moderate Ahead: How Is the Effectiveness of a New Drug Determined?

Subject: Chapter 1

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Chapter: Chapter 02 - Quiz

Multiple Choice

1. The minimization of bias and confounding in clinical trials is obtained through the use of which of the following?

A) Screening of study participants during recruitment to eliminate variation among participants B) The establishment of stringent inclusion criteria ensuring participants that are all similar C) The elimination of variation through the establishment of detailed exclusion criteria D) Randomization of study participants to make groups comparable in all respects Ans: D Complexity: Easy Ahead: Randomized Study Designs Subject: Chapter 2

2. A researcher is interested in determining the current prevalence of rheumatoid arthritis in the United States. Which type of study would be most useful in estimating the prevalence of rheumatoid arthritis in the United States?

A) A nested cohort study B) A cross-sectional survey C) A randomized clinical trial D) A case-crossover study Ans: B Complexity: Difficult Ahead: The Cross-Sectional Survey Subject: Chapter 2

3. A number of patients have been admitted to a particular hospital with similar symptoms and the cause of the illness is unknown. Which type of study design would be most helpful in determining the cause of the illness?

A) A randomized trial B) A case series C) A retrospective cohort D) A case-control study Ans: B

Complexity: Difficult Ahead: The Case Report/Case Series Subject: Chapter 2

4. Misclassification bias is most likely to be observed in which study type?

A) A randomized control trial B) A cross-sectional survey C) A prospective cohort D) A case-control study Ans: D Complexity: Easy Ahead: The Case-Control Study Subject: Chapter 2

5. A novice researcher noted that during summertime there is a positive association between the increase in ice cream sales and the increase in the number of drownings; however, there is no logical explanation for why ice cream sales would be responsible for the increased incidence of drowning. What phenomenon likely explains this type of observation?

A) Placebo effect B) Concurrency C) Confounding D) Misclassification Bias Ans: C Complexity: Moderate Ahead: Vocabulary Subject: Chapter 2

True/False

1. True or False? An active-control trial is the best option for researchers hoping to test a newly devised therapy for a life-threatening illness among individuals with the illness, when a previously devised treatment is available for the illness.

Ans: True Complexity: Moderate Ahead: Randomized Study Design Subject: Chapter 2

2. True or False? The application of treatment among participants in an experimental study is a key difference between an experimental study and an observational study.

Ans: True Complexity: Moderate Ahead: Randomized Study Designs

Subject: Chapter 2

3. True or False? Intention-to-treat analysis for a study is only conducted among individuals who fully complied with a study’s protocols.

Ans: False Complexity: Easy Ahead: Vocabulary Subject: Chapter 2

4. True or False? Extremely rare side effects of medications studied in clinical trials are more likely to be observed in cohort studies conducted during post marketing-surveillance because of the limited number of participants in clinical trials.

Ans: True Complexity: Difficult Ahead: More on Clinical Trials Subject: Chapter 2

5. True or False? The wash-out period is included in a crossover trial so that any therapeutic effects of the first treatment are removed, prior to the administration of the second treatment.

Ans: True Complexity: Easy Ahead: The Crossover Trial Subject: Chapter 2

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Chapter: Chapter 03 - Quiz

Multiple Choice

1. Assuming 320,000 individuals develop Lyme disease each year, what is the attributable risk for the cumulative incidence of Lyme disease that comes from tick bites, if 300,000 of the new cases reported each year come from tick bites?

A) 6.25% B) 6.67% C) 16.00% D) 93.75% Ans: D Complexity: Moderate Ahead: Difference Measures: Risk Difference and Population Attributable Risk Subject: Chapter 3

2. Which statistical property make odds ratios the ideal measurement for case-control studies?

A) Its insensitivity to confounding factors B) Its insensitivity to variance C) Its insensitivity to sampling error D) Its insensitivity to bias Ans: B Complexity: Easy Ahead: Ratios: Relative Risk, Odds Ratio, and Rate Ratio Subject: Chapter 3

3. Longitudinal cohort studies that produce data measured in person-time are particularly subject to which of the following forms of statistical anomaly?

A) Type one censoring B) Type two censoring C) Sampling bias D) Recall bias Ans: A Complexity: Easy Ahead: Issues with Person-Time Data

Subject: Chapter 3

4. A disease that has a low prevalence but high incidence rate is best described as which of the following types of diseases?

A) A noncontagious acute illness B) A contagious acute illness C) A noncontagious chronic illness D) A contagious chronic illness Ans: B Complexity: Difficult Ahead: Relationships Between Prevalence and Incidence Subject: Chapter 3

5. A simple random sample of 25,000 individuals are surveyed in order to determine the prevalence of individuals that contracted the flu in the past year. Assuming 4,250 individuals indicated they had been diagnosed with the flu at some point in the past year, what is the prevalence of flu for the past year, as indicated from the survey participants?

A) 1.70% B) 8.30% C) 17.0% D) 83.0% Ans: C Complexity: Moderate Ahead: Prevalence Subject: Chapter 3

True/False

1. True or False? Loss of study participants in longitudinal studies can make estimating the cumulative incidence of a disease more difficult.

Ans: True Complexity: Easy Ahead: Problems Estimating the Cumulative Incidence Subject: Chapter 3

2. True or False? Relative risk is an ideal form of measurement for a retrospective study design because it allows researchers to recruit both individuals with the outcome of interest and individuals without the outcome of interest, then match individuals from each of the respective groups to individuals of the other group in order to determine if a specific exposure caused the outcome of interest.

Ans: False Complexity: Difficult Ahead: Ratios: Relative Risk, Odds Ratio, and Rate Ratio Subject: Chapter 3

3. True or False? An absolute difference calculation is ideal when calculating the risk difference between two categorical variables.

Ans: True Complexity: Difficult Ahead: Comparing the Extent of Disease Between Groups Subject: Chapter 3

4. True or False? A group of 250 women over the age of 40 are recruited for a study to determine the effects that calcium has on bone health. Half of the participants are given a calcium supplement and the other half are given a placebo. If 13 women on calcium develop osteomalacia and 27 women not on the placebo develop osteomalacia, the relative risk for developing osteomalacia for women over 40 on a calcium supplement is 0.48 when compared to those women not taking a calcium supplement. This indicates that taking calcium has no effect on the population of interest’s health because the relative risk is less than 1.0.

Ans: False Complexity: Difficult Ahead: Ratios: Relative Risk, Odds Ratio, and Rate Ratio Subject: Chapter 3

5. True or False? The public health department in a particular county with 157,237 residents has documented 629 cases of HIV; 157 individuals were diagnosed in the past year. Thus, the cumulative incidence for HIV in this particular county is approximately 0.1.

Ans: False Complexity: Moderate Ahead: Incidence Subject: Chapter 3

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Chapter: Chapter 04 - Quiz

Multiple Choice

1. Marital status is best defined as which of the following types of variables?

A) Dichotomous variable B) Ordinal variable C) Categorical variable D) Continuous variable Ans: C Complexity: Moderate Ahead: Ordinal and Categorical Variables Subject: Chapter 4

2. A study is being conducted to determine the prevalence of lung cancer in a population and the researchers want to note the frequency of each particular stage of cancer among the members of the population who have lung cancer; in this case the stage of cancer is best defined as which of the following types of variables?

A) Dichotomous variable B) Ordinal variable C) Categorical variable D) Continuous variable Ans: B Complexity: Moderate Ahead: Ordinal and Categorical Variables Subject: Chapter 4

3. A researcher decides to take a random sample of individuals from the population and then track their sugar intake. Assuming the data collected on each individual will be classified into different levels of intake including little to no sugar intake, moderate sugar intake, and high sugar intake, which type of graph would allow the researcher to best represent the data they have collected?

A) Box plot B) Bar chart C) Histogram D) Pie chart

Ans: C Complexity: Moderate Ahead: Histograms for Ordinal Variables Subject: Chapter 4

4. Calculate the mean and standard deviation and interpret your findings for the following set of data showing the diastolic blood pressure measurements for a sample of 9 individuals: 61, 63, 64, 69, 71, 77, 80, 81, and 95.

A) On average, the average distance of an individual data point is approximately 10.93 diastolic pressure points from the mean diastolic pressure of 73.44.

B) On average, the average distance of an individual data point is approximately 119.53 diastolic pressure points from the mean diastolic pressure of 73.44.

C) On average, the average distance of an individual data point is approximately 10.93 diastolic pressure points from the mean diastolic pressure of 71.

D) On average, the average distance of an individual data point is approximately 119.53 diastolic pressure points from the mean diastolic pressure of 71.

Ans: A Complexity: Difficult Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

5. What is the median blood glucose level of the following data set collected from 8 individuals: 89, 95, 99, 102, 107, 108, 111, and 119?

A) 97.00 B) 103.75 C) 104.50 D) 109.50 Ans: C Complexity: Moderate Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

True/False

1. True or False? Bar charts are best used to display the information on data collected from nonmeasurable qualitative variables.

Ans: True Complexity: Easy Ahead: Bar Charts for Categorical Variables Subject: Chapter 4

2. True or False? Box plots are the best way to graphically represent the data obtained from research studies that focus on measuring the outcomes for variables considered to exist on a quantitative continuum.

Ans: True Complexity: Easy Ahead: Box-Whisker Plots for Continuous Variables Subject: Chapter 4

3. True or False? The standard deviation of any data set is the equivalent of the sample variance of the data set squared.

Ans: False Complexity: Easy Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

4. True or False? The mean is the best measure of central tendency for a data set measuring low-density lipoprotein (LDL) in which the individual measures of LDL were 100, 101, 105, 107, 109, 110, and 111.

Ans: True Complexity: Difficult Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

5. True or False? The best measure of central tendency for a data set containing a high number of singlesided outliers is the mean and the standard deviation.

Ans: False Complexity: Difficult Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

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Chapter: Chapter 05 - Quiz

Multiple Choice

1. Assume a researcher decides to contact individuals by telephone in order to survey them on their consumption of fruits and vegetables and decides to call and survey every 31st individual whose phone number is listed in the phonebook. What type of sampling method best describes the researcher’s sampling methodology?

A) Simple random sampling B) Systematic sampling C) Stratified sampling D) Convenience sampling Ans: B Complexity: Easy Ahead: Probability Sampling: Systematic Sampling Subject: Chapter 5

2. Assuming the below results were obtained in a study used to test the accuracy of the rapid diagnostic test for influenza, calculate and interpret the sensitivity of the rapid diagnostic influenza test.

Frequency of Individuals Who Screened Positive Frequency of Individuals Who Screened Negative

Frequency of Flu Cases

Frequency of Non-Flu Cases

47

10

43

100

A) When the rapid diagnostic influenza test is used, 52.22% of individuals who have the flu test positive for the flu.

B) When the rapid diagnostic influenza test is used, 90.91% of individuals who have the flu test positive for the.

C) When the rapid diagnostic influenza test is used, 47.78% of individuals who have the flu test positive for the flu.

D) When the rapid diagnostic influenza test is used, 9.09% of individuals who have the flu test positive for the flu.

Ans: A Complexity: Difficult Ahead: Sensitivity and Specificity Subject: Chapter 5

3. Assume a cardiovascular surgeon has implanted 13 pacemakers in his patients from a new batch of pacemakers that have been found to have a defect that causes them to stop working. If each pacemaker has a 23.47% chance that it will stop working, what is the probability that all the patients’ pacemakers will work the way they are supposed to?

A) 1.19e-7 B) .0527 C) .4730 D) .5270 Ans: B Complexity: Moderate Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

4. Assume a researcher wanted to know the probability that an individual’s systolic blood pressure would fall below 157 and the researcher found that the z-score corresponding to the 157 systolic blood pressure is 1.62. What is the probability that a random individual’s systolic blood pressure would fall below 157?

A) .0526 B) .4740 C) .5260 D) .9474 Ans: D Complexity: Easy Ahead: A Probability Model for a Continuous Outcome: The Normal Distribution Subject: Chapter 5

5. Assuming you obtained a random sample of blood glucose levels from 32 individuals from a population and the mean of the population is 120 and the standard deviation of the sample is 15, calculate the probability that the mean blood glucose levels for the sample population will be above 127.

A) .0041 B) .4100 C) .5900 D) .9959 Ans: A Complexity: Moderate Ahead: Sampling Distributions Subject: Chapter 5

True/False

1. True or False? If a study utilizes a simple random sampling method, that means each member of the population of interest was equally likely to be selected as a study participant.

Ans: True

Complexity: Easy Ahead: Probability Sampling: Simple Random Sampling Subject: Chapter 5

2. True or False? Sensitivity and specificity are both forms of conditional probability.

Ans: True Complexity: Moderate Ahead: Sensitivity and Specificity Subject: Chapter 5

3. True or False? The probability of an individual developing prostate cancer is independent of the sex of the individual.

Ans: False Complexity: Moderate Ahead: Independence Subject: Chapter 5

4. True or False? A clinical trial studying the effects of new antibiotic, which is suspected to be a curative treatment for drug-resistant syphilis, is likely to demonstrate a binomial distribution.

Ans: Ture Complexity: Difficult Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

5. True or False? A test used to measure the concentration of inflammatory markers in an individual’s blood is being researched. Assuming the test quantifies the concentration of the inflammatory markers in the blood and there are an infinite number of outcome possibilities, a study would likely demonstrate that the inflammatory markers for the population follow a normal, or non-normal, distribution pattern, depending on the results obtained from the study.

Ans: True Complexity: Difficult Ahead: A Probability Model for a Continuous Outcome: The Normal Distribution Subject: Chapter 5

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Chapter: Chapter 06 - Quiz

Multiple Choice

1. Assume researchers are trying to find out the mean concentration levels of a specific drug in a population of individuals’ blood during a clinical trail. The researchers find that the sample population has a mean concentration of 6.7 mcg/mL with a standard deviation of 1.3 mcg/mL. Calculate a 95% confidence interval for the mean concentration level of the medication for the population’s blood and interpret it.

A) The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 4.152 mcg/mL and 9.248 mcg/mL. B) The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 4.555 mcg/mL and 8.845 mcg/mL. C) The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 4.568 mcg/mL and 8.832 mcg/mL. D) The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 4.5615 mcg/mL and 8.8385 mcg/mL. Ans: A Complexity: Difficult Ahead: Introduction to Estimation Subject: Chapter 6

2. Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.

A) The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.

B) The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67.

C) The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.

D) The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.

Ans: D

Complexity: Difficult Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

3. A researcher has collected the blood samples of 29 individuals and found that the mean hemoglobin concentration for the sample of individuals is 13.9 grams per deciliter and the standard deviation is 1.43 grams per deciliter. Calculate a 95% confidence interval for the mean hemoglobin concentration for the population.

A) (13.36, 14.44) B) (13.38, 14.42) C) (10.98, 16.82) D) (11.10, 16.70) Ans: A Complexity: Moderate Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

4. Calculate the point estimate for a phase three clinical trial for a medication used to treat psoriasis, if 1790 patients show improvement of their psoriasis symptoms and 448 individuals did not show improvement of their psoriasis symptoms.

A) .2002 B) .2503 C) .7497 D) .7998 Ans: D Complexity: Moderate Ahead: Confidence Intervals for One Sample, Dichotomous Outcome Subject: Chapter 6

5. A phase three clinical trial for a new medication proposed to treat depression has 1191 participants. If all these individuals are from the group of individuals who were given the medication and 759 individuals who received the medication experienced improvement in their symptoms of depression, construct a 90% confidence interval for the true proportion of individuals on the medication who experienced improvement in their symptoms of depression.

A) (.363, .417) B) (.335, .363) C) (.623, .651) D) (.610, .664) Ans: C Complexity: Moderate Ahead: Confidence Intervals for One Sample, Dichotomous Outcome Subject: Chapter 6

True/False

1. True or False? Before conducting a confidence interval for the mean difference between two independent samples, a researcher should check to make sure the ratio between both sample’s variance is between 0.5 and 2.0.

Ans: True Complexity: Easy Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

2. True or False? When calculating a confidence interval for one sample with a continuous outcome and the sample contains 30 or fewer individuals, then a t-score should be used in place of a z-score.

Ans: False Complexity: Easy Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

3. True or False? The margin of error for a confidence interval for a population is equivalent to the standard deviation times the z-score value, or t-score value depending on the size of the population, for the probability of interest times the standard deviation of the population.

Ans: True Complexity: Easy Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

4. True or False? A researcher compares the BMI of two populations of individuals from different socioeconomic backgrounds and finds that the proportion of individuals considered obese and from a poor background is .37 (n = 112), and the proportion of individuals considered obese and from an affluent background is .27 (n = 87); a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).

Ans: True Complexity: Moderate Ahead: Confidence Intervals for the Risk Difference Subject: Chapter 6

5. True or False? Confidence intervals for relative risks and odds ratios require the usage of the natural log in their formula.

Ans: True Complexity: Easy Ahead: Confidence Intervals for the Odds Ratio Subject: Chapter 6

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Chapter: Chapter 07 - Quiz

Multiple Choice

1. A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians’ offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. The researcher’s hypothesis, for a level of significance of 5%, should resemble which of the following sets of hypothesis?

A) H0: p > .039; H1: p = .039; alpha= .05 B) H0: p = .039; H2: p > .039; alpha= .05 C) H0: p > .039; H1: p = .039; alpha= .95 D) H0: p = .039; H2: p > .039; alpha= .95 Ans: B Complexity: Easy Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

2. A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians’ offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. Calculate the z value for the test statistic.

A) z = - 1.12 B) z = 1.09 C) z = 0.92 D) z = -57.53 Ans: A Complexity: Moderate Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

3. A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians’ offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. For a level of significance of 5%, what should the researcher’s decision rule look like?

A) Reject H0 if z is less than or equal to -1.645.

B) Reject H0 if z is greater than or equal to 1.645.

C) Reject H0 if z is less than or equal to -1.96.

D) Reject H0 if z is greater than or equal to 1.96.

Ans: A Complexity: Easy Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

4. A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians’ offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. What should the researcher’s conclusion be for a 5% significance level?

A) We reject H0 at the 5% level because -57.53 is less than -1.96. We do have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.

B) We fail to reject H0 at the 5% because .092 is less than 1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.

C) We fail to reject H0 at the 5% because 1.09 is less than 1.96. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.

D) We fail to reject H0 at the 5% because -1.12 is greater than -1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.

Ans: D Complexity: Difficult Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

5. A new drug to treat psoriasis has been developed and is in clinical testing. Assume that those individuals given the drug are examined before receiving the treatment and then again after receiving the treatment to determine if there was a change in their symptom status. If the initial results showed that 2.0% of individuals entered the study in remission, 77.0% of individuals entered the study with mild symptoms, 16.0% of individuals entered the study with moderate symptoms, and 5.0% entered the study

with severe symptoms calculate and interpret a chi-squared test to determine if the drug was effective treating psoriasis given the information below from the final examination.

Number of Participants

Remission (No Symptoms of Psoriasis)

Mild Symptoms of Psoriasis

Moderate Symptoms of Psoriasis

Severe Symptoms of Psoriasis

Total Number of Participants to Receive the Drug

380

520

95

5

1000

A) We reject H0 because 6628.08 is greater than 5.99. We have statistically significant evidence at the alpha equals .05 level to show that the distribution of the severity of psoriasis cases at the end of the clinical trial for the sample is different from the distribution of the severity of psoriasis cases prior to the administration of the drug, suggesting the drug is effective.

B) We reject H0 because 6628.08 is greater than 7.81. We have statistically significant evidence at the alpha equals .05 level to show that the distribution of the severity of psoriasis cases at the end of the clinical trial for the sample is different from the distribution of the severity of psoriasis cases prior to the administration of the drug, suggesting the drug is effective.

C) We reject H0 because 6628.08 is greater than 9.49. We have statistically significant evidence at the alpha equals .05 level to show that the distribution of the severity of psoriasis cases at the end of the clinical trial for the sample is different from the distribution of the severity of psoriasis cases prior to the administration of the drug, suggesting the drug is effective.

D) We reject H0 because 6628.08 is greater than 11.07. We have statistically significant evidence at the alpha equals .05 level to show that the distribution of the severity of psoriasis cases at the end of the clinical trial for the sample is different from the distribution of the severity of psoriasis cases prior to the administration of the drug, suggesting the drug is effective.

Ans: B Complexity: Difficult Ahead: Tests with One Sample, Categorical and Ordinal Outcomes Subject: Chapter 7

True/False

1. True or False? For a two-tailed test using z values at the .05% significance level we reject H0 if z < 1.960 or if z > 1.960.

Ans: True Complexity: Easy Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

2. True or False? Assume a researcher recruits 150 African American and Caucasian individuals taking warfarin to determine if there is a difference in the mean dosage of the medication needed to cause a decrease in their INR blood test. If the mean dosage for 75 Caucasian individuals required to get their INR blood test in range is 6.1 mg with a standard deviation of 1.7 mg and the mean dosage for 75 African American individuals required to get their INR blood test in range is 4.3 mg with a standard deviation of 0.9 mg, the Sp value obtained while calculating the test statistic is approximately 1.14 mg.

Ans: True

Complexity: Moderate Ahead: Tests with Two Independent Samples, Continuous Outcome Subject: Chapter 7

3. True or False? Assume a researcher recruits 150 African American and Caucasian individuals taking warfarin to determine if there is a difference in the mean dosage of the medication needed to cause a decrease in their INR blood test. If the mean dosage for 75 Caucasian individuals required to get their INR blood test in range is 6.1 mg with a standard deviation of 1.7 mg and the mean dosage for 75 African American individuals required to get their INR blood test in range is 4.3 mg with a standard deviation of 0.9 mg, the z value obtained while calculating the test statistic is approximately 9.60.

Ans: True Complexity: Moderate Ahead: Tests with Two Independent Samples, Continuous Outcome Subject: Chapter 7

4. True or False? Assume a researcher recruits 150 African American and Caucasian individuals taking warfarin to determine if there is a difference in the mean dosage of the medication needed to cause a decrease in their INR blood test. If the mean dosage for 75 Caucasian individuals required to get their INR blood test in range is 6.1 mg with a standard deviation of 1.7 mg and the mean dosage for 75 African American individuals required to get their INR blood test in range is 4.3 mg with a standard deviation of 0.9 mg, the decision rule for a 10% level of significance would be to reject H0 if z < -1.645 or z > 1.645.

Ans: True Complexity: Moderate Ahead: Tests with Two Independent Samples, Continuous Outcome Subject: Chapter 7

5. True or False? H0 for an ANOVA test often states that all the mean values from the different independent samples are equal.

Ans: True Complexity: Easy Ahead: Tests with More than Two Independent Samples, Continuous Outcome Subject: Chapter 7

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Chapter: Chapter 08 - Quiz

Multiple Choice

1. A researcher is conducting a study to determine the mean trough dosage of medication for a population. Assuming a previous study was conducted for the same medication and the mean trough dose was found to be 490 mg with a standard deviation of 40 mg, calculate the margin of error for a 95% confidence interval assuming the previous study enrolled 350 individuals.

A) E = ± 4.19 B) E = ± 3.52 C) E = ± 0.22 D) E = ± 78.40 Ans: A Complexity: Moderate Ahead: Issues in Estimating Sample Size for Confidence Intervals Estimates Subject: Chapter 8

2. A researcher is conducting a study to determine the mean trough dosage of medication for a population. Assume a previous study was conducted for the same medication and the mean trough dose was found to be 490 mg with a standard deviation of 40 mg. If the researcher wants to be 95% confident the true mean trough dosage of the medication is within 10 mg of the true mean trough dosage, what sample size is needed?

A) n = 7 B) n = 8 C) n = 44 D) n = 62 Ans: D Complexity: Moderate Ahead: Sample Size for One Sample, Continuous Outcome Subject: Chapter 8

3. A researcher is conducting a study to determine the mean trough dosage of medication for a population. Assume a previous study was conducted for the same medication and the mean trough dose was found to be 490 mg with a standard deviation of 40 mg. If the researcher wants to be 95% confident the true mean trough dosage of the medication is within 10 mg of the true mean trough dosage, what sample size is needed if the study is predicted to have an 88% retention rate?

A) n = 8 B) n = 50 C) n = 55 D) n = 71 Ans: D Complexity: Moderate Ahead: Sample Size for One Sample, Continuous Outcome Subject: Chapter 8

4. A researcher wants to calculate the prevalence of Alzheimer’s among members of a specific community who are 65 years of age and older. The researcher needs to know how many individuals who are 65 years of age or older need to be recruited for the study to ensure the estimated prevalence will be within 1.0% of the true proportion. Calculate the sample size needed by the researcher if a national study has shown 11.11% of individuals 65 years of age have Alzheimer’s.

A) n = 3,794 B) n = 2,673 C) n = 6,549 D) n = 152 Ans: C Complexity: Moderate Ahead: Sample Size for One, Sample Dichotomous Outcome Subject: Chapter 8

5. A clinical trial is being conducted in order to determine the efficacy of a new drug that will be used to treat rheumatoid arthritis. The efficacy of the medication will not only be determined by the physical improvement of symptoms but will also be determined by using a blood test to examine the concentration of C-reactive protein (an inflammatory marker) in an individual’s blood. If the researcher wants a margin of error for the level of C-reactive protein to be less than or equal to 2.0 mg/d and if the standard deviation for C-reactive protein concentrations among arthritis patients was previously documented at 7 mg/dL, how many patients should be recruited for each group of individuals in the study, assuming a 95% confidence interval will be used to quantify the mean differences between the control group and the treatment group?

A) n for the treatment group = 95 and n for the control group = 95 B) n for the treatment group = 48 and n for the control group = 48 C) n for the treatment group = 47 and n for the control group = 48 D) n for the treatment group = 48 and n for the control group = 47 Ans: A Complexity: Difficult Ahead: Sample Sizes for Two Independent Samples, Continuous Outcome Subject: Chapter 8

True/False

1. True or False? To calculate the finalized n for a study, one should take the total number of participants needed to ensure the desired confidence interval and divide it by the proportion of individuals expected to be retained throughout the course of the study.

Ans: True Complexity: Easy Ahead: Sample Size for One Sample, Continuous Outcome Subject: Chapter 8

2. True or False? A researcher wants to be sure the mean difference in the change in blood pressure has a margin of error no more than 5 points and the difference in the standard deviation between the mean blood pressure points from the first medication used to treat high blood pressure and the second medication used to treat high blood pressure is 14 points. The desired sample size required to ensure a 95% confidence interval for the proposed study used to compare the efficacy of two medications used to treat high blood pressure during a cross-over trial is n = 31.

Ans: True Complexity: Difficult Ahead: Sample Size for Matched Samples, Continuous Outcome Subject: Chapter 8

3. True or False? A researcher wants to estimate the impact prenatal care during pregnancy can have on premature deliveries by conducting a retrospective case-control study on new moms. If the prevalence of premature births is approximately 10.9%, the researcher should enroll a total of 585 women in the study if the researcher wants to construct a 90% confidence interval for the difference in proportions that has a margin of error of no more than 3%.

Ans: False Complexity: Difficult Ahead: Sample Sizes for Two Independent Samples, Dichotomous Outcome Subject: Chapter 8

4. True or False? It is important for researchers to account for attrition or loss of participants during followup.

Ans: True Complexity: Easy Ahead: Sample Sizes for Two Independent Samples, Dichotomous Outcome Subject: Chapter 8

5. True or False? The effect size is the difference in the parameter of interest that represents a clinically meaningful difference.

Ans: True Complexity: Easy Ahead: Issues in Estimating Sample Size for Hypothesis Testing Subject: Chapter 8

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Chapter: Chapter 09 - Quiz

Multiple Choice

1. A specific medication used to prevent strokes, heart attacks, and blood clots requires a different dosage of medication for members of the African American population than the Caucasian population because a specific gene affects the way the drug is metabolized within the body. This is an example of which of the following?

A) Confounding B) Effect modification C) Selection bias D) Differential bias Ans: B Complexity: Difficult Ahead: Confounding and Effect Modification Subject: Chapter 9

2. A new and relatively expensive medication is released into the population to treat type II diabetes. A doctor notices that poor patients are less likely to see effects from the medication than more wealthy patients, but after conducting a survey the doctor finds the poor patients are less likely to fully comply with their medication regimen because they cannot afford to take the medication on a regular basis. This is an example of which of the following?

A) Confounding B) Statistical interaction C) Selection bias D) Recall bias Ans: B Complexity: Difficult Ahead: Confounding and Effect Modification Subject: Chapter 9

3. Research has found that circumcision has a protective effect and helps prevent HIV in men who have sex with women, but circumcision does not seem to have the same protective effect helping to prevent HIV in men who have sex with men. This is an example of which of the following?

A) Confounding B) Effect modification

C) Selection bias D) Recall bias Ans: B Complexity: Difficult Ahead: Confounding and Effect Modification Subject: Chapter 9

4. A researcher notes that there seems to be a difference in the prevalence of high cholesterol among individuals who smoke and consume diets high in processed food and the prevalence of high cholesterol among individuals who do not smoke and do not consume diets high in processed foods. Use the appropriate hypothesis to test for independence of two independent variables presented here at the 5% significance level to ensure confounding has not influenced the study’s results. Then interpret your response.

Diet Low in Processed Foods

Non-smoker Smoker Total

Normal Cholesterol

High Cholesterol

Total

124 69 193

55 152 207

179 221 400

Diet High in Processed Foods Non-smoker Smoker Total

Normal Cholesterol

High Cholesterol

Total

64 98 162

85 153 238

149 251 400

A) The chi square value of 37.724 is higher than the chi square value of 3.84, therefore we can accept H0 at the 5% level and reject H1, which states that smoking status and the amount of processed foods in an individual’s diet are not independent of one another.

B) The chi square value of 37.724 is higher than the chi square value of 3.84, therefore we can accept H0 at the 5% level and reject H1, which states that smoking status and the incidence of high cholesterol are not independent of one another C) The chi square value of 37.724 is higher than the chi square value of 3.84, therefore we can reject H0 at the 5% level in favor of H1, which states that smoking status and the incidence of high cholesterol are not independent of one another.

D) The chi square value of 37.724 is higher than the chi square value of 3.84, therefore we can reject H0 at the 5% level in favor of H1, which states that smoking status and the amount of processed foods in an individual’s diet are not independent of one another.

Ans: D Complexity: Difficult Ahead: Confounding and Effect Modification Subject: Chapter 9

5. A researcher notes that there seems to be a difference in the prevalence of individuals who are medication adherent and have high levels of education along with a high health literacy and the prevalence of individuals who are not medication adherent and have low levels of education along with a low health literacy. Use the appropriate hypothesis to test for independence of two independent variables

presented here at the 5% significance level to ensure confounding has not influenced the study’s results.

Then interpret your response.

Low Level of Education

Low Health Literacy High Health Literacy Total

Low Medication Adherence 91 9 100

High Medication Adherence 9 291 300

Total 100 300 400

High Level of Education

Low Health Literacy High Health Literacy Total

Low Medication Adherence 96 4 100

High Medication Adherence 4 296 300

Total 100 300 400

A) The chi square value of 2577.533 is higher than the chi square value of 3.84, therefore we can reject H0 in favor of H1, which states that an individual’s level of education and medication adherence status are not independent of one another.

B) The chi square value of 2577.533 is higher than the chi square value of 3.84, therefore we can accept H0 and reject H1, which states that an individual’s level of health literacy and medication adherence status are not independent of one another.

C) The chi square value of 2577.533 is higher than the chi square value of 3.84, therefore we can accept H0 and reject H1, which states that an individual’s level of education and level of health literacy status are not independent of one another.

D) The chi square value of 2577.533 is higher than the chi square value of 3.84, therefore we can reject H0 in favor of H1, which states that an individual’s level of education and health literacy status are not independent of one another.

Ans: D Complexity: Difficult Ahead: Confounding and Effect Modification Subject: Chapter 9

True/False

1. True or False? An r value of –0.3 indicates a weak negative association.

Ans: True Complexity: Easy Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 9

2. True or False? An r value of 0.5 indicates a positive moderate correlation.

Ans: True Complexity: Easy

Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 9

3. True or False? A linear regression equation and multiple linear regression equations can be used to calculate y if one is given the x values. However, a logistic regression equation cannot be used to calculate y when one is given x value.

Ans: False Complexity: Moderate Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 9

4. True or False? Multiple logistic regression analysis applies when there is a single dichotomous outcome and more than one independent variable.

Ans: True Complexity: Easy Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 9

5. True or False? Multivariable methods include a number of specific procedures to simultaneously assess the relationships between several exposure or risk factor variables and a single outcome.

Ans: True Complexity: Easy Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 9

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Chapter: Chapter 10 - Quiz

Multiple Choice

1. A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05.

Old Drug New Drug Old Drug

Pain Rating as Reported by Patients 1 3 3 4 6 1 2 3 3 7 Total Sample (Ordered Smallest to Largest) New Drug Old Drug New Drug

Ranks Old Drug

New Drug

R1=

R2=

A) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.

B) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 14.5 is greater than the critical U value of 2.

C) We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.

D) We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 14.5 is greater than the critical U value of 2.

Ans: A Complexity: Difficult Ahead: Tests with Two Independent Samples Subject: Chapter 10

2. A new chemotherapy drug is released to treat leukemia and researchers suspect that the drug may have fewer side effects than the most commonly used drug to treat leukemia. The two drugs have equivalent efficacy. In order to determine if a larger study should be conducted to look into the prevalence of side effects for the two drugs, set up a Mann-Whitney U test at the alpha equals .05 level and interpret its results.

Old Drug New Drug

Number of Reported Side-Effects 0 1 3 3 5 0 0 1 2 4

Old Drug

New Drug

Total Sample (Ordered Smallest to Largest) Old Drug New Drug

Ranks Old Drug

New Drug

R1=

R2=

A) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

B) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

C) We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

D) We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

Ans: B Complexity: Difficult Ahead: Tests with Two Independent Samples Subject: Chapter 10

3. A new medication is being developed to treat severe morning sickness in pregnant women. The information below was generated from a small sample size (n = 6) and shows the number of times a woman with morning sickness vomited both before and after treatment. Set up and interpret the results of a sign test at the alpha equals .05 level to determine if there is a difference in symptoms before and after treatment.

Pregnant Woman 1 2 3 4 5 6

Before Treatment 8 10 6 8 11 8

After Treatment 3 7 5 10 10 2

Difference

Sign

A) We fail to reject H0, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 1 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

B) We fail to reject H0, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 5 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

C) We reject H0 in favor of H1, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 1 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

D) We reject H0 in favor of H1, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 5 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

Ans: A Complexity: Difficult Ahead: Tests with Matched Samples Subject: Chapter 10

4. A new medication is being developed to treat severe nausea and vomiting among chemotherapy patients. The information below was generated from a small sample size (n = 11) and shows the number of times a chemotherapy patient vomited both before and after treatment due to the side effects of chemotherapy. Set up and interpret the results of a sign test at the alpha equals .05 level to determine if there is a difference in symptoms before and after treatment.

Chemotherapy Patient 1 2 3 4 5 6 7 8 9 10 11

Before Treatment 9 12 14 9 8 11 15 12 7 9 8

After Treatment

Difference

Sign

3 5 7 4 2 3 7 8 8 5 7

A) We fail to reject H0, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 1 is less than the critical value 2 for a sign test with a population of only 11 individuals.

B) We fail to reject H0, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 10 is greater than the critical value 2 for a sign test with a population of only 11 individuals.

C) We reject H0 in favor of H1, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 1 is less than the critical value 2 for a sign test with a population of only 11 individuals.

D) We reject H0 in favor of H1, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 10 is greater than the critical value 2 for a sign test with a population of only 11 individuals.

Ans: C Complexity: Difficult

Ahead: Tests with Matched Samples Subject: Chapter 10

5. A researcher is conducting a study on the palliative care of patients at a specific facility to determine how their chronic pain symptoms change after entering the palliative care environment. This study is aimed at determining the effectiveness of a standardized treatment protocol for the patients entering into the palliative care environment. To do this, the researcher is comparing the pain scores of individuals before treatment and after treatment. Set up a Wilcoxon signed-ranks test and interpret it at the alpha equals .05 level.

Patient

Before Treatment

After Treatment

1 2 3 4 5 6 7 8 9

9 10 7 8 6 9 6 7 9

4 5 3 5 7 5 4 3 4

Value of Differences

Ordered Absolute Values of Differences

Ranks

Sign Rank

A) We fail to reject H0, which states the median difference in the pain scores before and after treatment are equal because 1 is less than the critical value 10 for a Wilcoxon signed-ranks test with a population of only 11 individuals.

B) We fail to reject H0, which states the median difference in the pain scores before and after treatment are equal because 45 is greater than the critical value 44 for a Wilcoxon signed-ranks test with a population of only 11 individuals.

C) We reject H0 in favor of H1, which states the median difference in pain scores before and after treatment are not equal because 1 is less than the critical value 10 for a Wilcoxon signed-ranks test with a population of only 11 individuals.

D) We reject H0 in favor of H1, which states the median difference in pain scores before and after treatment are not equal because 44 is greater than the critical value 10 for a Wilcoxon signed-ranks test with a population of only 11 individuals.

Ans: C Complexity: Difficult Ahead: Tests with Matched Samples Subject: Chapter 10

True/False

1. True or False? A Kurskal-Wallis test is used to compare a continuous outcome in more than two independent samples.

Ans: True

Complexity: Easy Ahead: Summary Subject: Chapter 10

2. True or False? H0 for a Mann-Whitney U test is always that the two populations are equal.

Ans: True Complexity: Moderate Ahead: Summary Subject: Chapter 10

3. True or False? When performing a Mann-Whitney U test, one should always use the lower value of the calculated U values to compare to the critical U value while making the decision rule.

Ans: True Complexity: Easy Ahead: Tests with Two Independent Samples Subject: Chapter 10

4. True or False? H0 for the sign test always states that the mean difference between the matched or paired samples is zero.

Ans: False Complexity: Moderate Ahead: Summary Subject: Chapter 10

5. True or False? The test statistic for a sign test is always the smaller of the number of positive or negative signs.

Ans: True Complexity: Easy Ahead: Summary Subject: Chapter 10

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Chapter: Chapter 11 - Quiz

Multiple Choice

1. The survival curve below was constructed from a study that followed 7 individuals being treated with prednisone for inflammatory conditions over a period of 8 months. Assuming the event described is the point in time the individuals developed prednisone-induced hypertension and those individuals who made it to 8 months concluded the study without prednisone-induced hypertension, calculate and interpret the proportion of individuals who suffered from prednisone-induced hypertension at the end of the study.

A) 14.3% of individuals in the study did not develop prednisone-induced hypertension.

B) 14.3% of individuals in the study did not develop prednisone-induced hypertension during the time frame in which the study was being conducted.

C) 85.7% of individuals in the study did not develop prednisone-induced hypertension.

D) 85.7% of individuals in the study did not develop prednisone-induced hypertension during the time frame in which the study was being conducted.

Ans: D Complexity: Difficult Ahead: Estimating the Survival Function Subject: Chapter 11

2. The assumption that participant number 3 in the study below never developed the event of interest would likely lead to which of the following statistical errors?

A) Right censoring B) Left censoring C) Noninformative censoring D) Statistical censoring Ans: A Complexity: Moderate Ahead: Introduction to Survival Data Subject: Chapter 11

3. The survival curve below was constructed from a study that followed 7 individuals being treated with prednisone for inflammatory conditions over a period of 8 months. Assume the event described is the point in time the individuals developed prednisone-induced hypertension. Those individuals who made it to 8 months concluded the study without prednisone-induced hypertension; however, one participant developed hypertension 3 months later. Calculate and interpret Sp.

A) 14.3% of individuals in the study did not develop prednisone-induced hypertension.

B) 14.3% of individuals in the study did not develop prednisone-induced hypertension during the time frame in which the study was being conducted.

C) 0.00% of individuals in the study did not develop prednisone-induced hypertension.

D) 0.00% of individuals in the study did not develop prednisone-induced hypertension during the time frame in which the study was being conducted.

Ans: C Complexity: Difficult Ahead: Estimating the Survival Function Subject: Chapter 11

4. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results.

Time in Years

Number at Risk, Nt

0 1 2 3

20 20 17 16

Number of Deaths, Dt

Number Censored, Ct

Survival Probability 1

3 2

1 1

A) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85.

B) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study.

C) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment.

D) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study and for individuals who decided against all forms of treatment.

Ans: B Complexity: Difficult

Ahead: Estimating the Survival Function Subject: Chapter 11

5. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 2 using the Kaplan-Meir approach and interpret the results.

Time in Years

Number at Risk, Nt

0 1 2 3

20 20 17 16

Number of Deaths, Dt

Number Censored, Ct

Survival Probability 1

3 2

1 1

A) The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85.

B) The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study.

C) The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment.

D) The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study and for individuals who decided against all forms of treatment.

Ans: B Complexity: Difficult Ahead: Estimating the Survival Function Subject: Chapter 11

True/False

1. True or False? Assume the below life table was constructed from following individuals who were diagnosed with slow-progressing form of prostate cancer and decided not to receive treatment of any form. The calculated survival probability for year 3, if the Kaplan-Meir approach is used to calculate the survival probability, is approximately 0.7438.

Time in Years

Number at Risk, Nt

0 1 2 3

20 20 17 16

Ans: True Complexity: Difficult Ahead: Estimating the Survival Function Subject: Chapter 11

Number of Deaths, Dt

Number Censored, Ct

3 2

1 1

Survival Probability 1

2. True or False? Greenwood’s formula allows one to calculate the standard error of the survival estimates for a particular study.

Ans: True Complexity: Easy Ahead: Estimating the Survival Function Subject: Chapter 11

3. True or False? According to the survival curve below, at 2 years of time the probability of survival is approximately 90%.

Ans: True Complexity: Moderate Ahead: Estimating the Survival Function Subject: Chapter 11

4. True or False? According to the survival curve below, the probability of survival at 8 years of time is approximately 60%.

Ans: False Complexity: Moderate Ahead: Estimating the Survival Function Subject: Chapter 11

5. True or False? One of the most popular regression techniques for survival analysis is Cox proportional hazards regression. Cox proportional hazards regression is used to relate several risk factors or exposures, considered simultaneously, to survival time.

Ans: True Complexity: Easy Ahead: Cox Proportional Hazards Regression Analysis Subject: Chapter 11

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Chapter: Chapter 12 - Quiz

Multiple Choice

1. Which graphic representation could a researcher use to help determine if a continuous variable followed a normal distribution?

A) Histogram B) Bar chart C) Pie chart D) Box plot Ans: A Complexity: Moderate Ahead: Displaying Data and Distributions Subject: Chapter 12

2. Which graphic display can be key in communicating complex study protocols?

A) CONSORT charts B) Bubble map C) Stem plots D) Study outline Ans: A Complexity: Moderate Ahead: Participant Flow Charts Subject: Chapter 12

3. Column titles in a table should describe which of the following?

A) The independent variable B) The dependent variable C) The covariate variable D) The grouping variable Ans: D Complexity: Easy Ahead: Components of a Table Subject: Chapter 12

4. Which graph would be most useful in determining the change in two variables over time?

A) A histogram B) A bar chart C) A line chart D) A flow chart Ans: C Complexity: Moderate Ahead: Trends and Line Charts Subject: Chapter 12

5. Which type of statistical information or graph would be most helpful in determining whether the baseline characteristics of a study group are well balanced?

A) A bar chart B) Descriptive statics C) A box-whisker plot D) A flow chart Ans: B Complexity: Moderate Ahead: Tabulating Statistical Significance Subject: Chapter 12

True/False

1. True or False? Using a 95% confidence interval to describe an odds ratio allows other researchers to determine if the results were statistically significant because a statistically significant odds ratio confidence interval will not include the number 1.

Ans: True Complexity: Difficult Ahead: Tabulating Regression Results Subject: Chapter 12

2. True or False? The r2 value and a least squares regression line can be an excellent way to demonstrate the degree of correlation between two variables, and the type of association between the two variables.

Ans: True Complexity: Difficult Ahead: Displaying Associations Among Variables Subject: Chapter 12

3. True or False? Box-whisker plots are useful tools in comparing the mean and the distribution of two or more variables broken down into different categories.

Ans: True Complexity: Difficult Ahead: Figures to Compare Estimates Among Groups Subject: Chapter 12

4. True or False? Variable names and units of measurement should be specified clearly and accurately.

Ans: True Complexity: Easy Ahead: Components of a Table Subject: Chapter 12

5. True or False? Good tables have clear and concise titles.

Ans: True Complexity: Easy Ahead: Components of a Table Subject: Chapter 12

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Chapter: Midterm

Multiple Choice

1. The relative risk of developing lung cancer among individuals who smoke is 15.0. Which of the following is the most accurate interpretation of this information?

A) Individuals who have lung cancer are 15.0% more likely to smoke than individuals who do not have lung cancer.

B) Individuals who have lung cancer are 15.0 times more likely to smoke than individuals who do not have lung cancer.

C) Individuals who smoke are 15.0 times more likely to develop lung cancer than individuals who do not smoke.

D) Individuals who smoke are 15.0% more likely to develop lung cancer than individuals who do not smoke.

Ans: C Complexity: Moderate Ahead: How Is the Rate of Development of a New Disease Estimated?

Subject: Chapter 1

2. A healthcare provider notices an outbreak of foodborne illness among individuals who attended a holiday cookout. Which study type would be most beneficial in identifying the source of the outbreak?

A) A case series B) A retrospective cohort study C) A cross-sectional survey D) A case-control study Ans: A Complexity: Difficult Ahead: The Case Report/Case Series Subject: Chapter 2

3. A researcher hopes to measure the exposure a large number of individuals who have already developed lung cancer had to secondhand smoke throughout their lifetime. Which study design may prove useful in helping the researcher measure the exposure the individuals had to second hand smoke?

A) A case series B) A retrospective cohort study C) A prospective cohort study

D) A case-control study Ans: B Complexity: Difficult Ahead: The Cohort Study Subject: Chapter 2

4. A researcher has a hypothesis that a specific drug may have a higher prevalence of side effects among members of the African American population than members of the Caucasian population. Which statistical technique might the researcher want to use when designing a study to test their hypothesis?

A) Randomization B) Crossover matching C) Matching D) Stratification Ans: D Complexity: Difficult Ahead: Vocabulary Subject: Chapter 2

5. A new drug is released to market and it has been determined that the drug is responsible for causing hypertension among those individuals who take the drug. If 30,276 individuals were prescribed the drug in its first year on the market and 17,620 individuals developed hypertension, what is the point prevalence of hypertension among those individuals prescribed the drug, after the drug’s first year on the market?

A) 0.00582 B) 0.05820 C) 0.58200 D) 5.82000 Ans: C Complexity: Moderate Ahead: Prevalence Subject: Chapter 3

6. After attending a church cookout, a number of the attendees are admitted to the emergency room with nausea, vomiting, and diarrhea. After discovering all the individuals admitted to the ER consumed the egg salad at the event, the leftover egg salad was tested and found to be positive for salmonella. If 83 individuals consumed the egg salad and 49 individuals were admitted to the ER with salmonella, what was the cumulative incidence of salmonella assuming that the 49 individuals admitted to the ER were the only ones to be affected by the bacteria?

A) 0.041 B) 0.059 C) 0.410 D) 0.590 Ans: D Complexity: Moderate Ahead: Incidence Subject: Chapter 3

7. Drug manufactures of Drug X, which was released on the market 5 years ago to treat Crohn’s disease, have noticed that many individuals treated with the drug have developed drug-induced lupus. A cohort study was conducted for post-marketing surveillance. It has documented that 6 individuals have developed drug-induced lupus over the course of the past 5 years. If 1 individual developed the disease at the 1-year mark, 3 developed the disease at the 2-year mark, 1 developed the disease at the 3-year mark, and the final individual developed the disease at the 4-year mark, what is the incidence rate of drug-induced lupus?

A) 0.0429 B) 0.4290 C) 0.5710 D) 0.9571 Ans: B Complexity: Moderate Ahead: Incidence Rate Subject: Chapter 3

8. In which situation would it be most appropriate to use the mean of the set of numbers to describe the data set instead of the median?

A) 152, 157, 159, 163, 164, 165, 976 B) 0, 899, 906, 912, 915, 917, 919 C) 0, 57, 847, 859, 866, 866, 872 D) 165, 165, 177, 178, 186, 199, 211 Ans: D Complexity: Moderate Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

9. A 95% confidence interval for relative risk of developing a bacterial infection after having a surgery is (3.71, 5.33) when comparing a non-laparoscopic surgery procedure to a laparoscopic surgery procedure.

This indicates which of the following?

A) The researchers are confident because the probability that these results would occur is somewhere between 3.71% and 5.33%.

B) The researchers are confident that the probability that these results would occur is somewhere between 0.371% and 0.533%.

C) The researchers are 95% confident that the increased risk of developing an infection is between 3.71 to 5.33 times higher among individuals who had the non-laparoscopic surgery when compared to those individuals who received the laparoscopic surgery.

D) The researchers are 95% confident that the risk of developing an infection is between 3.71 to 5.33 times higher among individuals who had the laparoscopic surgery when compared to those individual who received the non-laparoscopic surgery.

Ans: C Complexity: Difficult Ahead: Confidence Intervals for the Relative Risk Subject: Chapter 6

10. Which of the following accurately represents a 95% confidence interval for a sample of 5 individuals whose blood glucose levels were 98, 111, 105, 120, and 147?

A) (153.5, 78.9) B) (78.9, 153.5) C) (63.4, 169.0) D) (169.0, 63.4) Ans: C Complexity: Moderate Ahead: Introduction to Estimation Subject: Chapter 6

11. With a binomial distribution with n = 25 and p = 0.48, which is larger?

A) P(12 successes) B) P(9 successes) C) P(20 successes) D) P(10 successes) Ans: A Complexity: Difficult Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

True/False

1. True or False? Biostatistics is integral to the practice of public health because it allows public health professionals to accurately monitor and track the prevalence of disease within a population.

Ans: True Complexity: Easy Ahead: What Is Biostatistics?

Subject: Chapter 1

2. True or False? The margin of error in a research study is indicative of the precision and accuracy of the research results obtained in the study.

Ans: True Complexity: Moderate Ahead: How Is the Rate of Development of a New Disease Estimated?

Subject: Chapter 1

3. True or False? An active-controlled trial allows researchers to offer participants a placebo in place of an alternative treatment method that has been previously proven to be effective.

Ans: False Complexity: Easy Ahead: The Randomized Controlled Trial (RCT) or Clinical Trial

Subject: Chapter 2

4. True or False? Incidence reflects the likelihood of developing a disease among a group of participants free of the disease who are considered at risk of developing the disease over a specified observation period; prevalence involves estimating the proportion of people who have disease at a point in time.

Ans: True Complexity: Easy Ahead: Incidence Subject: Chapter 3

5. True or False? If the odds of catching the flu among individuals who take vitamin C is 0.0342 and the odds of catching the flu among individuals not taking vitamin C is 0.2653, then the individuals not taking vitamin C are 7.7573 times more likely to catch the flu than individuals taking vitamin C. Ans: True Complexity: Difficult Ahead: Ratios: Relative Risk, Odds Ratio, and Rate Ratio Subject: Chapter 3

6. True or False? Histograms are often used to display categorical data, while bar charts are commonly used to display variables that fall on a measurable continuum.

Ans: False Complexity: Easy Ahead: Bar Charts for Categorical Variables Subject: Chapter 4

7. True or False? Variability within a sample is oftentimes measured using sample variance.

Ans: False Complexity: Easy Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

8. True or False? A newly proposed endoscopy method used to screen for colon cancer is tested among a random sample of the population. Given that 16 individuals from a test population of 100,000 individuals has colon cancer and 14 individuals test positive for colon cancer, the researchers should determine the sensitivity of the newly proposed screening method is .875.

Ans: True Complexity: Moderate Ahead: Sensitivity and Specificity Subject: Chapter 5

9. True or False? A newly developed medical procedure to prevent death in women who give birth and experience eclampsia has a 97.5% success rate of saving the woman’s life. If a doctor uses this medical procedure in 6 women who experience eclampsia and have no other comorbid conditions, the probability that all 6 women will survive is approximately 0.859.

Ans: True Complexity: Moderate Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

10. True or False? The mean measure of high density lipoprotein (HDL), or good cholesterol, is 54 with a standard deviation of 17 in patients over age 50. If the HDL values are obtained from a sample of 32 individuals, the probability of getting a mean HDL value over 62 is 0.049.

Ans: False Complexity: Moderate Ahead: Sampling Distributions Subject: Chapter 5

11. True or False? If there are outliers, then the mean will be greater than the median.

Ans: False Complexity: Moderate Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

12. True or False? The 90th percentile of the standard normal distribution is 1.645.

Ans: False Complexity: Moderate Ahead: Normal Distributions Subject: Chapter 6

13. True or False? The mean is the 50th percentile of any normal distribution.

Ans: True Complexity: Easy Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

14. True or False? The mean is a better measure of location when there are no outliers.

Ans: True Complexity: Easy Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

15. True or False? Case-control study, prospective cohort study, cross-over trial, and retrospective cohort study are all examples of observational study designs.

Ans: False Complexity: Easy Ahead: Observational Study Designs Subject: Chapter 2

16. True or False? For the standard normal distribution, Q3 = 0.675.

Ans: True Complexity: Difficult Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

Essay

1. The risk of hepatoma among alcoholics without cirrhosis of the liver is 24%. Suppose we observe 7 alcoholics without cirrhosis. What is the probability that exactly one of these 7 people have a hepatoma?

Ans: .3237 Complexity: Difficult Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

2. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean of 120 and a standard deviation of 16. What proportion of patients have glucose levels exceeding 115? If a patient has a glucose level of 140, what percentile is this? What is the probability that the mean glucose level exceeds 115 in a sample of 12 patients?

Ans: a) .6217; b) 89th; c) 8599 Complexity: Moderate Ahead: A Probability Model for a Continuous Outcome: The Normal Distribution; Sampling Distributions Subject: Chapter 5

3. The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Using the following data, compute the mean BMI, the standard deviation of BMI, the median BMI and the Q1 and Q3. Are there outliers in the distribution of BMI? Justify your answer.

25

27

31

33

26

28

38

41

24

32

35

40

Ans: a) 31.7; b) 5.9; 31.5; c) Q1 = 26.5 and Q3 = 36.5; d) Check Q1-1.5(Q3-Q1) = 26.5-1.5(36.5-26.5) = 11.5, Q3+1.5(Q3-Q1) = 36.5+1.5(36.5-26.5) = 51.5; e) There are no outliers.

Complexity: Moderate Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

4. The following table shows the numbers of patients classified as underweight, normal weight, overweight and obese according to their diabetes status. What is the probability that a patient selected at random is overweight? What is the probability that they are obese and diabetic? What proportion of the diabetics are obese? What proportion of normal weight patients are not diabetic? What proportion of patients are normal weight or underweight?

Diabetes No Diabetes

Underweight 8 12

Normal Weight 34 85

Overweight 65 93

Obese 43 40

Ans: a) .42; b) .11; c) .29; d) .71; e) .37 Complexity: Moderate Ahead: Basic Concepts; Conditional Probability Subject: Chapter 5

5. A new non-invasive screening test is proposed that is claimed to be able to identify patients with impaired glucose tolerance based on a battery of questions related to health behaviors. The new test is given to 75 patients. Based on each patient’s responses to the questions they are classified as positive or negative for impaired glucose tolerance. Each patient also submits a blood sample and their glucose tolerance status is determined. The results are tabulated below. What is the sensitivity of the screening test? What is the false positive fraction of the screening test?

Screening Test Positive Negative

Impaired Glucose Tolerance 17 8

Not Impaired 13 37

Ans: a) .68; b) .26 Complexity: Moderate Ahead: Sensitivity and Specificity Subject: Chapter 5

6. A study is conducted to test a new drug claimed to reduce diastolic blood pressure in adults with a history of coronary heart disease. What is the most efficient study to test whether the drug reduces diastolic blood pressure? Justify.

Ans: Clinical trial Complexity: Moderate Ahead: Randomized Controlled Trial Subject: Chapter 2

7. Approximately 30% of obese patients develop diabetes. Answer the following questions if a physician sees 10 patients who are obese: a) What is the probability that half of them will develop diabetes? b) What is the probability that none will develop diabetes? c) How many would you expect to develop diabetes?

Ans: a) .1029; b) .0282; c) 3 Complexity: Moderate Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

8. A study is run to investigate body mass index (BMI) in children living in urban neighborhoods. Based on the following data: compute the sample mean, the sample standard deviation, and the median.

29

26

24

32

30

22

27

28

31

Ans: a) 27.7; b) 3.3; c) 28 Complexity: Moderate Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

9. The following table shows the distribution of BMI in children living in United States and European urban neighborhoods. (The data are in millions.) What is the probability that a child selected at random is overweight? What is the probability that a child living in a U.S. urban neighborhood is overweight? What is the probability that a child living in a European urban neighborhood is overweight? What is the probability that a child lives in a U.S. urban neighborhood and is obese? What is the probability that a child is overweight and neighborhood location independent? Justify briefly.

Neighborhood United States Europe

Normal Weight 125 101

Overweight 50 42

Obese 40 21

Ans: a) .24; b) .23; c) .26; .11; d) Check P(overweight | US) = P(overweight), 0.23 ≠ 0.24; e) The child is not neighborhood location independent.

Complexity: Moderate Ahead: Basic Concepts; Conditional Probability; Independence Subject: Chapter 5

10. Suppose that the probability that a child living in an urban area in the United States is obese is 20%. If a social worker sees 15 children living in urban areas, answer the following: What is the probability that none are obese? What is the probability that 5 are obese?

Ans: a) .0352; b) .1032 Complexity: Moderate Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

11. Body mass index (BMI) in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2. Answer the following questions: a) A BMI between 25 and 30 is considered overweight. What proportion of children are overweight? b) A BMI of 30 or more is considered obese.

What proportion of children are obese? c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?

Ans: a) .2814; b) .1867; c) .3974 Complexity: Moderate Ahead: A Probability Model for a Continuous Outcome: The Normal Distribution; Conditional Probability Subject: Chapter 5

12. An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age).

Give two possible study designs and indicate the pros and cons of each. Then, provide your recommendation for the most efficient design.

Ans: One possible design is a cohort design where children with and without exposure to secondhand smoke would be recruited and followed for 5 years, at which point they would be classified as having or not having asthma. The major advantage of the cohort design is the ability to establish the temporal relationship between exposure and outcome (development of asthma). A second option is the casecontrol design where children with asthma and without asthma would be selected. Their exposure to secondhand smoke would then be assessed. An advantage of the case-control design is that there will be a sufficient number of children with asthma. A small number of outcome events (i.e., children with asthma) could be a problem with the cohort design. The case control design, however, suffers from various sources of bias, including recall bias. The most efficient design for this study is the cohort design.

Complexity: Moderate Ahead: Observational Studies Subject: Chapter 2

13. A study is run to estimate the incidence of atrial fibrillation (AF) in men and women over the age of 60.

Development of atrial fibrillation was monitored over a 10-year follow-up period. The data are summarized below. Using this data, compute the cumulative incidence of AF in men and in women, the relative risk of AF incidence comparing men to women, and the odds ratio of AF incidence comparing men and women.

Men Women

Developed AF 120 86

Did not Develop AF 6453 7074

Ans: a) men = 0.018; b) women = 0.012; c) 1.5; d) 1.58 Complexity: Moderate Ahead: Incidence; Ratios: Relative Risk, Odds Ratio, and Rate Ratio Subject: Chapter 3

14. The following data were collected in a survey of 8th graders and summarize their cell phone status.

What proportion of the 8th graders have cell phones? What proportion of the boys do not have cell phones? Is ownership of a cell phone independent of sex? Justify your answer. What proportion of smart phone users are boys?

Boys Girls

No cell phone 55 31

Conventional cell phone user 65 78

Smart phone user 35 27

Ans: a) .70; b) .35; c) Check P(no cell phone | boy) = P(no cell phone), 55/155 = 0.35 ≠ 86/291 = 0.30; d) Ownership of a cell phone is not independent of sex.; e) .56 Complexity: Moderate Ahead: Basic Concepts; Conditional Probability Subject: Chapter 5

15. A ferritin test is a popular test to measure a person’s current iron stores. In women, ferritin is approximately normally distributed with a mean of 89 ng/mL and a standard deviation of 23 ng/mL. What is the probability that a woman has a ferritin value of 100 or less? If a woman has a ferritin of 140, what percentile is this? If 50 women are tested, what is the probability that the mean ferritin exceeds 90?

Ans: a) .6844; b) 99th; c) .3783 Complexity: Moderate Ahead: A Probability Model for a Continuous Outcome: The Normal Distribution; Sampling Distributions Subject: Chapter 5

16. A pilot study is run to investigate the effect of a lifestyle intervention designed to increase medication adherence in patients with HIV. Medication adherence is measured as the percentage of prescribed pills that are taken over a one-week observation period. Ten patients with HIV agree to participate and their medication adherence before and after the intervention are shown below. Compute the following: a) differences in adherence before versus after the intervention for each participant, b) the mean difference in adherence before versus after the intervention, and c) the standard deviation of the difference in adherence before versus after intervention.

Participant ID 1 2 3 4 5 6 7 8 9 10

Before Intervention 75% 82% 66% 74% 88% 66% 51% 93% 88% 91%

After Intervention 80% 84% 70% 70% 90% 75% 60% 90% 90% 95%

Ans: a) Participant ID 1 2 3 4 5

Before Intervention 75% 82% 66% 74% 88%

After Intervention 80% 84% 70% 70% 90%

Difference 5 2 4 -4 2

6 7 8 9 10

66% 51% 93% 88% 91%

75% 60% 90% 90% 95%

9 9 -3 2 4

b) 3.0; c) 4.3 Complexity: Moderate Ahead: Confidence Intervals for Matched Samples, Continuous Outcome Subject: Chapter 6

17. The following table shows the results of a screening test hypothesized to detect persons at risk for side effects of a new cosmetic surgery. Compute the sensitivity of the test, the specificity of the test, the false positive fraction, and the false negative fraction.

Screen positive Screen negative

Side effects present 12 85

Side effects absent 6 204

Ans: a) .12; b) .97; c) .03; d) .88 Complexity: Moderate Ahead: Sensitivity and Specificity Subject: Chapter 5

18. A clinical trial designed to show the efficacy of a new drug in reducing progression to hypertension reports the following data. Using this information, compute the relative risk of progression to hypertension among patients receiving the new drug as compared to the placebo, the difference in proportions of patients progressing to hypertension between the two groups, and the odds ratio of progression to hypertension among patients receiving the new drug as compared to the placebo.

New Drug 200 14%

Sample size Progression to hypertension

Placebo 200 19%

Ans: a) .74; b) –.05; c) .70 Complexity: Moderate Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

19. The following are grade point averages measured in a sample of 8 undergraduate students who are applying to graduate schools in public health. Compute the sample mean, the sample standard deviation, and the sample median.

3.28

2.97

3.05

3.61

3.39

2.95

3.00

Ans: a) 3.17; b) .24; c) 3.075 Complexity: Easy Ahead: Descriptive Statistics for Continuous Variables

3.10

Subject: Chapter 4

20. The following table shows the results of a screening test hypothesized to identify persons at risk for a rare blood disease. Compute the sensitivity of the test, the specificity of the test, the false positive fraction, and the false negative fraction.

Screen Negative Screen Positive

No Disease 1274 51

Disease 28 45

Ans: a) .62; b) .96; c) .04; d) .38 Complexity: Moderate Ahead: Sensitivity and Specificity Subject: Chapter 5

21. The data shown below describe children in four countries in terms of adequate dental care. What is the probability that a child from the United States has adequate dental care? What is the probability that a child from France has adequate dental care? What proportion of children have inadequate dental care?

What proportion of children with inadequate dental care are from the United States?

United Kingdom United States France Mexico

Adequate Dental Care 2539 4563 1298 2874

Inadequate Dental Care 176 209 307 256

Ans: a) .96; b) .81; c) .08; d) .22 Complexity: Moderate Ahead: Conditional Probability Subject: Chapter 5

22. The mean total serum cholesterol level in women free of cardiovascular disease is 205 with a standard deviation of 19.2. What proportion of women have total serum cholesterol levels exceeding 200?

If values between the 5th and 95th percentiles are considered “normal,” what is the upper limit of normal?

If a sample of 10 women are analyzed, what is the probability that their mean total serum cholesterol levels exceeds 210?

Ans: a) .6026; b) 236.6; c) .2061 Complexity: Moderate Ahead: A Probability Model for a Continuous Outcome: The Normal Distribution; Sample Distributions Subject: Chapter 5

23. Four hundred melanoma patients were diagnosed according to the type of skin cancer and the location of the skin cancer. This data is presented below. What proportion of patients had superficial spreading melanoma? Of patients with a skin cancer on the trunk, what proportion had a nodular skin

cancer? What proportion of patients had a Hutchinson’s melanomic freckle on the extremities? Is type of skin cancer independent of location? Justify your answer.

Type Hutchinson’s melanomic freckle Indeterminate Nodular Superficial spreading melanoma Total

Head and Neck 22 11 19 16 68

Location Trunk 2 17 33 54 106

Extremities 10 28 73 115 226

Total 34 56 125 185 400

Ans: a) .436; b) .311; .025; c) Check P(nodular | trunk) = P(nodular), 0.311 ≠ 125/4000=0.3125; d) The type of skin cancer is not independent of location.

Complexity: Moderate Ahead: Conditional Probability; Independence Subject: Chapter 5

24. The gestation period for human births can be taken as normally distributed with a mean of 266 days and a standard deviation of 16 days. What is the probability that a randomly chosen baby had a gestation period of more than 280 days? If a gestation period is 276 days, what percentile among human births is this?

Ans: a) .1894; b) 74th Complexity: Moderate Ahead: A Probability Model for a Continuous Outcome: The Normal Distribution Subject: Chapter 5

25. The faculty and staff at Dana-Farber Cancer Institute in Boston are required to undergo a tuberculosis test each year. Use the following table to answer the questions below. If a Dana-Farber faculty or staff worker goes in to have a TB test, what is the chance of him/her getting a positive test result? What is the positive predictive value of the test?

Tuberculosis Yes No

Test Result

Total

Positive

4995

99,950

104,945

Negative

5

9,895,050

9,895,055

Total

5,000

9,995,000

10,000,000

Ans: a) .01; b) .048 Complexity: Moderate Ahead: Bayes Theorem Subject: Chapter 5

Import Settings: Base Settings: Brownstone Default Information Field: Complexity Information Field: Ahead Information Field: Subject Highest Answer Letter: D Multiple Keywords in Same Paragraph: No

Chapter: Final

Multiple Choice

1. Which of the following individuals is likely to be excluded from a clinical trial?

A) An individual with other diseases besides the disease of interest.

B) An individual whose data is considered to be an outlier.

C) An individual of who is considered to be a minority.

D) An individual who will have difficulty complying trial protocols.

Ans: A Complexity: Moderate Ahead: How Are Risk Factors or Characteristics That Might Be Related to the Development or Progression of Disease Identified?

Subject: Chapter 1

2. Randomization in a clinical trial is defined as which of the following?

A) The process by which individuals are coupled into groups for comparison in order to minimize bias and confounding.

B) The process by which individuals are assigned a number and are selected through the usage of a pattern which minimizes bias and confounding.

C) The process by which individuals are randomly assigned to a treatment or control group which minimizes bias and confounding.

D) The process by which individuals are asked to volunteer for a study which minimizes bias and confounding.

Ans: C Complexity: Easy Ahead: Randomized Study Designs Subject: Chapter 2

3. Assuming 50,000 individuals in the United States are diagnosed every year, and of those individuals diagnosed with HIV each year, approximately 33,500 individuals diagnosed with HIV are gay or bisexual males. What prevalence of the new HIV cases are from members of the population of gay or bisexual males?

A) 0.67% B) 6.70% C) 33.0%

D) 67.0% Ans: D Complexity: Moderate Ahead: Prevalence Subject: Chapter 3

4. Ethnicity (i.e., Hispanic versus non-Hispanic) is best described as which type of variable?

A) Dichotomous variable B) Ordinal variable C) Categorical variable D) Continuous variable Ans: A Complexity: Easy Ahead: Ordinal and Categorical Variables Subject: Chapter 4

5. A researcher wants to determine the sensitivity of mammograms to determine how effective they are at diagnosing women who have breast cancer. Assume the researcher obtained the above results from a study, calculate and interpret the sensitivity of mammograms for detecting breast cancer.

Frequency of Individuals Who Screened Positive Frequency of Individuals Who Screened Negative

Frequency of Breast Cancer Cases

Frequency of Non-Cancer Cases

12

5

6

77

A) A total of 66.67% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

B) A total of 93.90% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

C) A total of 70.59% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

D) A total of 92.77% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

Ans: A Complexity: Difficult Ahead: Sensitivity and Specificity Subject: Chapter 5

6. A researcher wants to compare the mean concentration of two medications considered biologically equivalent, i.e., two medications that are able to produce the same therapeutic effect at the same level of concentration in the blood. The group of individuals on medication one (n = 32) had a mean blood concentration of 21.7 micrograms per milliliter with a standard deviation of 8.7 micrograms per milliliter.

The group of individuals on medication two (n = 32) had a mean blood concentration of 19.4 micrograms per milliliter with a standard deviation of 5.2 micrograms per milliliter. Construct and interpret a 95%

confidence interval demonstrating the difference in means for the individuals on medication one when compared to the group of individuals on medication two.

A) The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 1.212 micrograms per milliliter and 5.812 micrograms per milliliter.

B) The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 4.867 micrograms per milliliter and 9.467 micrograms per milliliter.

C) The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 11.747 micrograms per milliliter and 16.347 micrograms per milliliter.

D) The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 3.477 micrograms per milliliter and 8.077 micrograms per milliliter.

Ans: A Complexity: Difficult Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

7. A researcher suspects that the actual prevalence of depression among children and adolescents is higher than was previously reported. The previously reported prevalence for depression among children and adolescents was 12.5%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of depression among children and adolescents by recruiting 100 total children or adolescents and tests them for depression using the DSM-5. The researcher determines that the prevalence of depression from the study is 12.9% and the standard deviation was 0.4. What should the researcher’s conclusion be for a 5% significance level?

A) We reject H0 at the 5% level because 10 is greater than 1.96. We do have statistically significant evidence to show the actual prevalence of depression among children and adolescents is above the previously reported prevalence of 12.5%.

B) We fail to reject H0 at the 5% because -10 is less than 1.645. We do not have statistically significant evidence to show the actual prevalence of depression among children and adolescents is above the previously reported prevalence of 12.5%.

C) We fail to reject H0 at the 5% because -10 is less than 1.96. We do not have statistically significant evidence to show the actual prevalence of depression among children and adolescents is above the previously reported prevalence of 12.5%.

D) We fail to reject H0 at the 5% because 10 is greater than -1.645. We do not have statistically significant evidence to show the actual prevalence of depression among children and adolescents is above the previously reported prevalence of 12.5%.

Ans: A Complexity: Difficult Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

8. A clinical trial is being conducted in order to determine the efficacy of a new drug used to treat Rheumatoid arthritis. The efficacy of the medication will not only be determined by the physical improvement of symptoms but also by using a blood test to examine the concentration C-reactive protein (an inflammatory marker) in an individual’s blood. If the researcher wants a margin of error for the level of C-reactive protein to be less than or equal to 3.0 mg/dL, and if the standard deviation for C-reactive protein concentrations among arthritis patients was previously documented at 8 mg/dL, how many

patients should be recruited for each group in the study assuming a 95% confidence interval will be used to quantify the mean differences between the control group and the treatment group?

A) n for the treatment group = 112; n for the control group = 111 B) n for the treatment group = 56; n for the control group = 57 C) n for the treatment group = 56; n for the control group = 56 D) n for the treatment group = 112; n for the control group = 112 Ans: D Complexity: Difficult Ahead: Sample Sizes for Two Independent Samples, Continuous Outcome Subject: Chapter 8

9. A researcher notes that there seems to be a difference in the prevalence of high blood pressure among college-educated individuals who consume low amounts of processed foods and the prevalence of individuals who only have a high school education and consume high amounts of processed foods. Use the appropriate hypothesis to test for the independence of the two independent variables presented here at the 5% significance level to ensure confounding has not influenced the study’s results. Then, interpret your response.

Diet Low in Processed Foods Normal BP

High BP

Total

College Education

124

55

179

High School Education

69

152

221

Total

193

207

400

Diet High in Processed Foods Normal BP

High BP

Total

College Education

64

85

149

High School Education

98

153

251

Total

162

238

400

A) The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we can accept H0 at the 5% level and reject H1, which states that level of education and the amount of processed foods in an individual’s diet are not independent of one another.

B) The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we can accept H0 at the 5% level and reject H1, which states that level of education and the incidence of high blood pressure are not independent of one another.

C) The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we can reject H0 at the 5% level in favor of H1, which states that level of education and the incidence of high blood pressure are not independent of one another.

D) The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we can reject H0 at the 5% level in favor of H1, which states that level of education and the amount of processed foods in an individual’s diet are not independent of one another.

Ans: D Complexity: Difficult Ahead: Confounding and Effect Modification Subject: Chapter 9

True/False

1. True or False? Researchers use active-controlled trials to test new medications that are used to treat a particular illness against old medications used to treat the same illness.

Ans: True Complexity: Moderate Ahead: Randomized Study Design Subject: Chapter 2

2. True or False? Assume approximately 1,500 cases of malaria are diagnosed in the United States each year among tourists and world travelers. If 1,470 of the cases are attributed to mosquito bites from out of the country each year, then the population attributable risk for the number of malaria cases caused by mosquito bites is 98.0%.

Ans: True Complexity: Moderate Ahead: Difference Measures: Risk Difference and Population Attributable Subject: Chapter 3

3. True or False? A researcher decides to take a random sample of the population and determine the ALT levels of the population, which fall on a continuum. A bar chart would be useful in determining if the ALT levels of the population are normally distributed.

Ans: False Complexity: Moderate Ahead: Histograms for Ordinal Variables Subject: Chapter 4

4. True or False? A stratified random sample can be used to ensure underrepresented populations are represented in a study.

Ans: True Complexity: Easy Ahead: Probability Sampling: Stratified Sampling Subject: Chapter 5

5. True or False? Assume a doctor uses a specific form of mesh to repair all hernias in his hernia patients. The makers of the mesh found there was an error that occurred while making the mesh, and the hernia mesh has a 45% chance of failure. The doctor has treated 7 patients with the mesh so far; thus, the probability that the mesh does not fail in all seven patients is .0152.

Ans: True

Complexity: Moderate Ahead: A Probability Model for a Discrete Outcome: The Binomial Distribution Subject: Chapter 5

6. True or False? It is important for researchers to account for attrition or loss of participants during followup.

Ans: True Complexity: Easy Ahead: Sample Sizes for Two Independent Samples, Dichotomous Outcome Subject: Chapter 8

7. True or False? An r value of .8 indicates a strong positive correlation.

Ans: True Complexity: Moderate Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 9

8. True or False? When performing a Mann-Whitney U test, one should always use the higher value of the calculated U values to compare to the critical U value while making the decision rule.

Ans: False Complexity: Easy Ahead: Tests with Two Independent Samples Subject: Chapter 10

9. True or False? Using a 95% confidence interval to describe an odds ratio and a relative risk ratio allows other researchers to determine if the results were statistically significant because a statistically significant odds ratio confidence interval will not include the number 1.

Ans: True Complexity: Moderate Ahead: Displaying Associations Among Variables Subject: Chapter 12

10. True or False? The margin of error is always greater than or equal to the standard error.

Ans: False Complexity: Moderate Ahead: Issues Estimating Sample Size For Confidence Intervals Estimates Subject: Chapter 8

11. True or False? If a test is run and p = 0.0356, then we can reject H0 at a = 0.01.

Ans: False Complexity: Moderate Ahead: Hypothesis Testing Procedures Subject: Chapter 7

12. True or False? If a 95% confidence interval for the difference in two independent means is (-4.5 to 2.1), then the point estimate is -2.1.

Ans: False Complexity: Moderate Ahead: Hypothesis Testing Procedures Subject: Chapter 7

13. True or False? If a 95% confidence interval for the difference in two independent means is (2.1 to 4.5), there is no significant difference in means.

Ans: False Complexity: Moderate Ahead: Confidence Intervals For Two Independent Samples, Continuous Outcome Subject: Chapter 6

14. True or False? If a 90% confidence interval for the mean is (75.3 to 80.9), we would reject H0: µ =70 in favor of H1: µ ≠ 70 at a = 0.05.

Ans: False Complexity: Moderate Ahead: Confidence Interval for One Independent Sample, Continuous Outcome Subject: Chapter 6

15. True or False? In logistic regression, the predictors are dichotomous, and the outcome is a continuous variable.

Ans: False Complexity: Moderate Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 10

16. True or False? When calculating a correlation coefficient between two continuous variables, the scales on which the variables are measured affect the value of the correlation coefficient.

Ans: False Complexity: Moderate Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 10

17. True or False? It is more difficult to reject a null hypothesis if we use a 10% level of significance compared with a 5% level of significance.

Ans: False Complexity: Easy Ahead: Introduction to Hypothesis Testing Subject: Chapter 7

18. True or False? The sample size required to detect an effect size of 0.25 is larger than the sample size required to detect an effect size of 0.50 with 80% power and a 5% level of significance.

Ans: True Complexity: Easy Ahead: Sample Size for One Sample, Continuous Outcome Subject: Chapter 8

Essay

1. The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and are participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Generate a 95% confidence interval estimate of the true BMI. 25

27

31

33

26

28

38

41

24

32

35

40

Ans: (27.95, 35.45) Complexity: Moderate Ahead: Confidence Intervals for One Sample, Continuous Outcome Subject: Chapter 6

2. How many subjects would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 2 units?

25

27

31

33

26

28

38

41

24

32

35

40

Ans: 34 Complexity: Moderate Ahead: Sample Size for One Sample, Continuous Outcome Subject: Chapter 8

3. The mean body mass index (BMI) in patients free of diabetes was reported as 28.2. An investigator conducting the study hypothesizes that the BMI in patients free of diabetes is higher. Based on the data, is there evidence that the BMI is significantly higher than 28.2? Use a 5% level of significance.

25

27

31

33

26

28

38

41

24

32

35

40

Ans: Reject H0 since 2.06 > 1.796. We have significant evidence, a = 0.05, to show that the mean is greater than 28.2.

Complexity: Moderate Ahead: Tests with One Sample, Continuous Outcome Subject: Chapter 7

4. Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator wants to test whether children with chronic bronchitis have restricted PEF. A sample of 40 children with chronic bronchitis is studied, and their mean PEF is 279 with a standard deviation of 71. Is there statistical evidence of a lower mean PEF in children with chronic bronchitis? Run the appropriate test at a = 0.05.

Ans: Reject H0 since -2.41 < -1.645. We have significant evidence, a = 0.05, to show that the mean is less than 306.

Complexity: Moderate Ahead: Tests with One Sample, Continuous Outcome Subject: Chapter 7

5. Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator conducts a study to investigate whether there is a difference in mean PEF in children with chronic bronchitis as compared to those without asthma or other respiratory conditions often have restricted PEF. Data on PEF are collected and summarized below. Based on the data, is there statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without? Run the appropriate test at a = 0.05.

Group Chronic Bronchitis No Chronic Bronchitis

Number of Children 25 25

Mean PEF 281 319

Std Dev PEF 68 74

Ans: Reject H0 since -1.89 < -1.677. We have significant evidence, a = 0.05, to show that a = 0.05 µ 1 < µ 2.

Complexity: Moderate Ahead: Tests with Two Independent Samples, Continuous Outcome Subject: Chapter 5

6. Using the data presented below, a) construct a 95% confidence interval for the mean PEF in children without chronic bronchitis; b) determine how many children would be required to ensure that the margin of error in (a) does not exceed 10 units.

Group Chronic Bronchitis No Chronic Bronchitis

Number of Children 25 25

Mean PEF 281 319

Std Dev PEF 68 74

Ans: a) (288.45, 349.55); b) n = 211 Complexity: Moderate Ahead: Confidence Intervals for One Sample, Continuous Outcome Subject: Chapter 6

7. A clinical trial is run to investigate the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and to a placebo. Pregnant women are enrolled and randomly assigned to receive either the experimental drug, the standard drug or a placebo. Women are followed through delivery and classified as delivering preterm (< 37 weeks) or not. The data are shown below.

Preterm Delivery Yes No

Experimental Drug 17 83

Standard Drug 23 77

Placebo 35 65

Is there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups? Run the test at a 5% level of significance.

Ans: Reject H0 since 8.953 > 5.99. We have significant evidence, a = 0.05, to show that treatment and preterm delivery are not independent.

Complexity: Moderate Ahead: Tests with One Sample, Categorical and Ordinal Outcomes Subject: Chapter 7

8. Using the data below, generate a 95% confidence interval for the difference in proportions of women delivering preterm in the experimental and standard drug treatment groups.

Preterm Delivery Yes No

Experimental Drug 17 83

Standard Drug 23 77

Placebo 35 65

Ans: (-0.17 to 0.05) Complexity: Moderate Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

9. Consider the data below. Previous studies have shown that approximately 32% of women deliver prematurely without treatment. Is the proportion of women delivering prematurely significantly higher in the placebo group? Run the test at a 5% level of significance.

Preterm Delivery Yes No

Experimental Drug 17 83

Standard Drug 23 77

Placebo 35 65

Ans: Do not reject H0 since 0.64 < 1.645. We do not have significant evidence, a = 0.05, to show that the proportion exceeds 32%.

Complexity: Moderate

Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

10. A study is run comparing HDL cholesterol levels between men who exercise regularly and those who do not. The data are shown below.

Regular Exercise Yes No

N 35 120

Mean 48.5 56.9

Std Dev 12.5 11.9

Generate a 95% confidence interval for the difference in mean HDL levels between men who exercise regularly and those who do not.

Ans: (-12.93 to -3.87) Complexity: Moderate Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcomes Subject: Chapter 6

11. A clinical trial is run to assess the effects of different forms of regular exercise on HDL levels in persons between the ages of 18 and 29. Participants in the study are randomly assigned to one of three exercise groups (Weight training, Aerobic exercise or Stretching/Yoga) and instructed to follow the program for 8 weeks. Their HDL levels are measured after 8 weeks and are summarized below.

Exercise Group Weight Training Aerobic Exercise Stretching/Yoga

N 20 20 20

Mean 49.7 43.1 57.0

Std Dev 10.2 11.1 12.5

Is there a significant difference in mean HDL levels among the exercise groups? Run the test at a 5% level of significance. HINT: SSerror = 7286.5.

Ans: Reject H0 since 7.56 > 3.18. We have significant evidence, a = 0.05, to show that the means are not all equal.

Complexity: Difficult Ahead: Tests with More Than Two Independent Samples, Continuous Outcome Subject: Chapter 7

12. Consider the data below. Suppose that in the aerobic exercise group we also measured the number of hours of aerobic exercise per week; the mean is 5.2 hours with a standard deviation of 2.1 hours. The sample correlation is -0.42. a) Estimate the equation of the regression line that best describes the relationship between number of hours of exercise per week and HDL cholesterol level (Assume that the dependent variable is HDL level). b) Estimate the HDL level for a person who exercises 7 hours per week. c) Estimate the HDL level for a person who does not exercise.

Exercise Group Weight Training Aerobic Exercise Stretching/Yoga

N 20 20 20

Mean 49.7 43.1 57.0

Std Dev 10.2 11.1 12.5

Ans: a) Ŷ = 54.6 - 2.22x ; b) 39.06; c) 54.6 Complexity: Difficult Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 9

13. The table below summarizes baseline characteristics of patients participating in a clinical trial. a) Are there any statistically significant differences in baseline characteristics between treatment groups? Justify your answer. b) Write the hypotheses and the test statistic used to compare ages between groups. (No calculations – just H0, H1 and form of the test statistic). c) Write the hypotheses and the test statistic used to compare % females between groups. (No calculations – just H0, H1 and form of the test statistic). d) Write the hypotheses and the test statistic used to compare % females between groups. (No calculations – just H0, H1 and form of the test statistic.)

Characteristic

Placebo (n = 125)

Experimental ( n =125)

P

54 + 4.5

53 + 4.9

0.7856

% Female

39%

52%

0.0289

% Less than High School Education

24%

22%

0.0986

% Completing High School

37%

36%

% Completing Some College

39%

42%

Mean (+ SD) Systolic Blood Pressure

136 + 13.8

134 + 12.4

0.4736

Mean (+ SD) Total Cholesterol

214 + 24.9

210 + 23.1

0.8954

% Current Smokers

17%

15%

0.5741

% with Diabetes

8%

3%

0.0438

Mean (+ SD) Age

Ans: a) The % female and % with diabetes are statistically significantly different between groups with p < 0.05 for each. b) H0: µ1 = µ2 H1: µ1 ≠ µ2

Z=

X1 - X 2 Sp

1 1 + n1 n 2

c) H0: p1 = p2 H1: p1 ≠ p2

Z=

p̂1 - p̂ 2 æ1 1 ö p̂(1 - p̂)çç + ÷÷ è n1 n 2 ø

d) H0: Treatment and educational level are independent. H1: Treatment and educational level are not

(O - E) 2 independent. χ = Σ E 2

Complexity: Moderate Ahead: Tests for Two or More Independent Samples, Categorical and Ordinal Variables Subject: Chapter 7

14. A study is designed to investigate whether there is a difference in response to various treatments in patients with Rheumatoid arthritis. The outcome is the patient’s self-reported effect of treatment. The data are shown below. Is there a significant difference in effect of treatment? Run the test at a 5% level of significance.

Treatment 1 Treatment 2 Treatment 3

Symptoms Worsened 22 14 9

No Effect 14 15 12

Symptoms Improved 14 21 29

Total 50 50 50

Ans: Reject H0 since 11.4 > 9.49. We have significant evidence, a = 0.05, to show that treatment and response are not independent.

Complexity: Difficult Ahead: Tests for Two or More Independent Samples, Categorical and Ordinal Subject: Chapter 7

15. Using the data below, suppose we focus on the proportions of patients who show improvement. Is there a statistically significant difference in the proportions of patients who show improvement between treatments 1 and 2. Run the test at a 5% level of significance.

Treatment 1 Treatment 2 Treatment 3

Symptoms Worsened 22 14 9

No Effect

Symptoms Improved

Total

14 15 12

14 21 29

50 50 50

Ans: Do not reject H0 since -1.96 < -1.47 < 1.96. We do not have significant evidence, a = 0.05, to show that there is a difference in the proportions of patients who show improvement between treatments 1 and 2.

Complexity: Difficult Ahead: Tests with Two Independent Samples, Dichotomous Outcome Subject: Chapter 7

16. An analysis is conducted to compare mean time to pain relief (measured in minutes) under four competing treatment regimens. Summary statistics on the four treatments are shown below.

Treatment A B

Sample Size 5 5

Mean Time to Relief 33.8 27.0

Sample Variance 17.7 15.5

C D

5 5

50.8 39.6

9.7 16.8

a) Complete the following ANOVA Table.

Source of Variation Between Groups Within Groups

SS

df

MS

F

3719.48

Total a) Write the decision rule. b) What is the conclusion? c) Write the hypotheses to be tested.

Ans: a) Source of Variation Between Groups Within Groups

SS 1524.4 3719.48

df 3 16

Total

5243.88

19

MS 508.1 232.47

F 2.19

b) Reject H0 if F > 3.24 c) Do not reject H0 since 2.19 < 3.24. We do not have significant evidence, a = 0.05, to show that there is a difference in means. d) H0: µA = µB = µC = µD a = 0.05 H1: Means are not all equal.

Complexity: Difficult Ahead: Tests with More Than Two Independent Samples, Continuous Outcome Subject: Chapter 7

17. The following data were collected in a clinical trial to compare a new drug to a placebo for its effectiveness in lowering total serum cholesterol. Generate a 95% confidence interval for the difference in mean total cholesterol levels between treatments.

Mean (SD) Total Serum Cholesterol % Patients with Total Cholesterol < 200

New Drug (n = 75)

Placebo (n = 75)

Total Sample (n = 150)

185.0 (24.5)

204.3 (21.8)

194.7 (23.2)

78.0%

65.0%

71.5%

Ans: (-26.66 to -11.94) Complexity: Moderate Ahead: Confidence Intervals for Two Independent Samples, Continuous Outcome Subject: Chapter 6

18. Using the data below, a) generate a 95% confidence interval for the proportion of all patients with total cholesterol < 200. b) How many patients would be required to ensure that a 95% confidence interval has a margin of error not exceeding 5%?

Ans: a) (0.643 to 0.787); b) n = 314 patients are needed Complexity: Moderate Ahead: Sample Size for One Sample, Dichotomous Outcome Subject: Chapter 8

19. A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Run the test at a 5% level of significance.

Subject 1 2 3 4 5 6

Initial Weight 155 142 176 180 210 125

Weight after 6 Weeks 157 145 180 175 209 126

Ans: Do not reject H0 since 0.5 < 2.015. We do not have significant evidence, a = 0.05, to show that there a significant increase in body weight following supplementation.

Complexity: Difficult Ahead: Confidence Intervals for One Sample, Continuous Outcome Subject: Chapter 6

20. The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo.

Characteristic*

New Drug

Age, years 45.2 (4.8) % Female 51% Annual Income, $000s 59.5 (14.3) % with Insurance 87% Disease Stage Stage I 35% Stage II 42% Stage III 23% *Table entries and Mean (SD) or %

Standard Drug

Placebo

p

44.9 (5.1) 55% 63.8 (16.9) 65%

42.8 (4.3) 57% 58.2 (13.6) 82%

0.5746 0.1635 0.4635 0.0352 0.0261

18% 37% 51%

33% 47% 20%

a) Are there any statistically significant differences in the characteristics shown among the treatments?

Justify your answer. b) Consider the test for differences in age among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only). c) Consider the test for differences in insurance coverage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only). d) Consider the test for differences in disease

stage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only).

Ans: a) % with insurance and disease stage are statistically significantly different between groups with p < 0.05 for each. b) H0: µ1 = µ2 = µ3 H1: Means are not all equal.

F=

MSB MSE

c) H0: Treatment and insurance coverage are independent.

H1: Treatment and insurance coverage are not independent. d) H0: Treatment and disease stage are independent.

H1: Treatment and disease stage are not independent, a = 0.05.

Complexity: Easy Ahead: Tests For Two or More Two Independent Samples, Categorical and Ordinal Variables Subject: Chapter 7

21. A small pilot study is run to compare a new drug for chronic pain to one that is currently available.

Participants are randomly assigned to receive either the new drug or the currently available drug and to report improvement in pain on a 5-point ordinal scale: 1 = Pain is much worse, 2 = Pain is slightly worse, 3 = No change, 4 = Pain improved slightly, 5 = Pain much improved. Is there a significant difference in self-reported improvement in pain? Use the Mann-Whitney U test with a 5% level of significance.

New Drug: Standard Drug:

4 2

5 3

3 4

3 1

4 2

2 3

Ans: Do not reject H0 because 9 > 5. We do not have statistically significant evidence, a = 0.05, to show that the populations of self-reported improvement in pain are not equal between treatments.

Complexity: Difficult Ahead: Tests with Two Independent Samples Subject: Chapter 10

22. A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children.

A total of 250 children are randomized to either the new drug or a placebo (125 per group). The mean age of children assigned to the new drug is 12.4 with a standard deviation of 3.6 years. The mean age of children assigned to the placebo is 13.0 with a standard deviation of 4.0 years. Is there a statistically significant difference in ages of children assigned to the treatments? Run the appropriate test at a 5% level of significance.

Ans: Do not reject H0 since -1.960 < -1.25 < 1.96. We do not have significant evidence, a = 0.05, to show that µ1 ≠ µ2.

Complexity: Difficult Ahead: Tests with Two Independent Samples, Continuous Outcome Subject: Chapter 7

23. A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children.

A total of 250 children are randomized to either the new drug or a placebo (125 per group). The mean

age of children assigned to the new drug is 12.4 with a standard deviation of 3.6 years. The mean age of children assigned to the placebo is 13.0 with a standard deviation of 4.0 years. Suppose that there are 63 boys assigned to the new drug group and 58 boys assigned to the placebo group. Is there a statistically significant difference in the proportions of boys assigned to the treatments? Run the appropriate test at a 5% level of significance.

Ans: Do not reject H0 since -1.96 < 0.63 < 1.96. We do not have significant evidence, a = 0.05, to show that there is a difference in the proportions of boys assigned to the treatments.

Complexity: Difficult Ahead: Tests for Two Independent Samples, Dichotomous Outcomes Subject: Chapter 7

24. A clinical trial is run to evaluate the effectiveness of a new drug to prevent preterm delivery. A total of n = 250 pregnant women agree to participate and are randomly assigned to receive either the new drug or a placebo, and they are followed through the course of pregnancy. Among 125 women receiving the new drug, 24 deliver preterm; among 125 women receiving the placebo, 38 deliver preterm. Construct a 95% confidence interval for the difference in proportions of women who deliver preterm.

Ans: (-.22, 0.00) Complexity: Moderate Ahead: Confidence Intervals for Two Independent Samples, Dichotomous Outcome Subject: Chapter 6

25. “Average adult Americans are about one inch taller, but nearly a whopping 25 pounds heavier than they were in 1960, according to a new report from the Centers for Disease Control and Prevention (CDC).

The bad news, says the CDC, is that average BMI (body mass index, a weight-for-height formula used to measure obesity) has increased among adults from approximately 25 in 1960 to 28 in 2002.” Boston is considered one of America’s healthiest cities. Is the weight gain since 1960 similar in Boston? A sample of n = 25 adults suggested a mean increase of 17 pounds with a standard deviation of 8.6 pounds. Is Boston statistically significantly different in terms of weight gain since 1960? Run the appropriate test at a 5% level of significance.

Ans: Reject H0 since -4.65 < -2.064. We have significant evidence, a = 0.05, to show that the mean is different than 25.

Complexity: Difficult Ahead: Tests with One Sample, Continuous Outcome Subject: Chapter 7

26. In 2007, the CDC reported that approximately 6.6 per 1000 (0.66%) children were affected with autism spectrum disorder. A sample of 900 children from Boston are tested, and 7 are diagnosed with autism spectrum disorder. Is the proportion of children affected with autism spectrum disorder higher in Boston as compared to the national estimate? Run the appropriate test at a 5% level of significance.

Ans: Do not reject H0 since 0.44 < 1.645. We do not have significant evidence, a = 0.05, to show that the proportion exceeds 0.66%.

Complexity: Moderate Ahead: Tests with One Sample, Dichotomous Outcome Subject: Chapter 7

27. A clinical trial is being planned to investigate the effect of a new experimental drug designed to reduce total serum cholesterol. Investigators will enroll participants with total cholesterol levels between 200-240.

The participants will be randomized to receive the new drug or a placebo and followed for 2 months, and the total cholesterol will be measured. Investigators plan to run a test of hypothesis and want 80% power to detect a difference of 10 points in mean total cholesterol levels between groups. They assume that 10% of the participants randomized will be lost over the 2-month follow-up. How many participants must be enrolled in the study? Assume that the standard deviation of total cholesterol is 18.5.

Ans: 120 total Complexity: Moderate Ahead: Sample Sizes for Two Independent Samples, Continuous Outcome Subject: Chapter 8

28. An observational study is conducted to investigate the association between age and total serum cholesterol. The correlation is estimated at r = 0.35. The study involves n = 125 participants. The mean (std dev) age is 44.3 (10.0) years with an age range of 35 to 55 years, and mean (std dev) total cholesterol is 202.8 (38.4). a) Estimate the equation of the line that best describes the association between age (as the independent variable) and total serum cholesterol. b) Estimate the total serum cholesterol for a 50-year old person. c) Estimate the total serum cholesterol for a 70-year old person.

Ans: a) Ŷ = 143.4 + 1.34x ; b) 210.4; c) 237.2 Complexity: Moderate Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 10

29. How is the slope coefficient (b1) in a simple linear regression different than the coefficient (b1) in a multiple linear regression model?

Ans: In a simple linear regression analysis, the slope represents the expected change in Y relative to a one unit change in X. In a multiple linear regression analysis, b1 is the expected change in Y relative to a one unit change in X1 holding the other predictors constant or adjusting (accounting for) the other predictors in the model.

Complexity: Moderate Ahead: Introduction to Correlation and Regression Analysis Subject: Chapter 10

30. When would a survival analysis model be used instead of a logistic regression model?

Ans: Survival analysis is used when the outcome is time to event. Logistic regression analysis is appropriate if the outcome is dichotomous (yes/no) and all participants are followed through the end of the study period.

Complexity: Difficult Ahead: Introduction to Survival Data Subject: Chapter 11

31. What is the appropriate statistical test to assess whether there is an association between obesity status (normal weight, overweight, obese) and 5-year incident cardiovascular disease (CVD)? Suppose each participant’s obesity status (category) is known along with whether they develop CVD over the next 5 years or not.

Ans: Here we would use the chi-square test of independence and compare the portions of normal weight, overweight and obese persons who develop CVD over 5 years. The data could be summarized in a 3x2 cross-tabulation.

Complexity: Easy Ahead: Tests For Two or More Two Independent Samples, Categorical and Ordinal Variables Subject: Chapter 7

32. An observational study is conducted to compare experiences of men and women between the ages of 50–59 years following coronary artery bypass surgery. Participants undergo the surgery and are followed until the time of death, until they are lost to follow-up, or up to 30 years, whichever comes first. The following table details the experiences of participating men and women. The data below are years of death or years of last contact for men and women. a) Estimate the Estimate the survival functions for each treatment group using the Kaplan-Meier approach. b) Test if there is a significant difference in survival between treatment groups using the log rank test and a 5% level of significance.

Men Year of Death 5 12 14 23 29

Women

Year of Last Contact 8 17 24 26 26 27 29 30 30 30

Year of Death 19 20 21 24

Year of Last Contact 4 9 14 15 17 19 21 22 24 25 30

Ans: a) Time, Months

Number at Risk in Placebo Group 1 N1t

5

15

Number at Risk in New Drug Group 2 N2t 14

12

13

13

26

1

1

0.500

0.500

14

12

13

25

1

1

0.480

0.520

19

10

10

20

1

0.500

0.500

Total Number at Risk Nt

Number of Events in Group 1 O1t

29

1

Number of Events in Group 2 O2t

1

1

Expected Number of Events in Group 1 E1t = N1t*(Ot/Nt).

0.517

Expected Number of Events in Group 2 E2t = N2t*(Ot/Nt).

0.483

Total Number of Events Ot

20

10

8

18

1

1

0.556

0.444

21

10

7

17

1

1

0.588

0.412

23

10

4

14

1

0.714

0.286

24

9

4

13

1

0.692

0.308

29

5

1

6

1

0.833

0.167

5.381

3.619

1 1 1 5

4

b) Do not reject H0 because 0.067 < 3.84. We do not have statistically significant evidence, a = 0.05, to show that the time to death is different between men and women.

Complexity: Difficult Ahead: Estimating the Survival Function Subject: Chapter 11

23. A random sample of 8 adults aged 30 years were asked how much they spent on medical costs in the year 2009. Using the following data, compute the sample mean, the sample standard deviation, the sample median, and the first and third quartiles.

300

140

5600

520

470

Ans: a) 1196.25; b) 1806.8; c) 580; d) Q1 = 385, Q3 = 950 Complexity: Easy Ahead: Descriptive Statistics for Continuous Variables Subject: Chapter 4

700

640

1200