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1 A table represents the number of students who passed or failed an aptitude test at two different campuses. East Campus West Campus Passed 39 45 Failed 61 55 In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed. What is the expected frequency of East Campus and passed? 48.3 students 42 students 50.5 students 39 students 2 The data below shows the heights in inches of 10 students in a class. Student Height, in inches Student 1 53 Student 2 52.5 Student 3 54 Student 4 51 Student 5 50.5 Student 6 49.5 Student 7 48 Student 8 53 Student 9 52 Student 10 50 The standard error of the sample mean for this set of data is __________. Answer choices are rounded to the hundredths place. 1.87
1.77 0.19 0.59 3 For a left-tailed test, the critical value of z so that a hypothesis test would reject the null hypothesis at 1% significance level would be __________. Answer choices are rounded to the hundredths place. -2.33 -3.09 -1.28 -1.03 4 A researcher has a table of data with four column variables and three row variables. The value for the degrees of freedom in order to calculate the statistic is __________. 12 11 6 3 5 Rachel recorded the number of calls she made at work during the week: Day Calls Monday 18 Tuesday 14 Wednesday 24 Thursday 16 She expected to make 18 calls each day. To answer whether the number of calls follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10) What is the chi-squared test statistic? Answers are rounded to the nearest hundredth. 3.27 4.61 1.52 3.11 6
Select the statement that correctly describes a Type II error. A Type II error occurs when the null hypothesis is rejected when it is actually true. A Type II error occurs when the null hypothesis is accepted when it is actually true. A Type II error occurs when the null hypothesis is accepted when it is actually false. A Type II error occurs when the null hypothesis is rejected when it is actually false. 7 Joe hypothesizes that the students of an elite school will score higher than the general population. He records a sample mean equal to 568 and states the hypothesis as μ = 568 vs μ > 568. What type of test should Joe do? Two-tailed test Joe should not do any of the types of tests listed Right-tailed test Left-tailed test 8 A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for males earning $100,000 or more annually and for females earning $80,000 or more annually. Out of 267 persons who replied to their survey, 32 are listed under this category. What is the standard error of the sample proportion? Answer choices are rounded to the hundredths place. 0.02 1.96 0.32 0.20 9 One condition for performing a hypothesis test is that the observations are independent. Mark is going to take a sample from a population of 400 students. How many students will Mark have to sample without replacement to treat the observations as independent? 300 40 360
80 10 What value of z* should be used to construct a 97% confidence interval of a population mean? Answer choices are rounded to the thousandths place. 2.17 1.96 1.65 1.88 11 Which of the following assumptions for a two-way ANOVA is FALSE? The variances of the populations must be equal. The groups must have the same sample size. The samples must be dependent. The sample populations must be normally or approximately normally distributed. 12 Joe is measuring the widths of doors he bought to install in an apartment complex. He measured 72 doors and found a mean width of 36.1 inches with a standard deviation of 0.3 inches. To test if the doors differ significantly from the standard industry width of 36 inches, he computes a z-statistic. What is the value of Joe's z-test statistic? 2.83 1.81 -2.83 -1.81 13 Which of the following is an example of a parameter? All of the members of the community watch group gave their availability to volunteer over the summer. 3.5% of the restaurant goers are given a survey to fill out. 9047 out of 531,310 citizens voted in the special election for city council.
Half of the receipts at the coffee shop include web address for giving feedback. 14 Mike tabulated the following values for heights in inches of seven of his friends: 65, 71, 74, 61, 66, 70, and 72. The sample standard deviation is 4.577. Select the 95% confidence interval for Mike's set of data. 59.95 to 76.91 64.19 to 72.67 59.95 to 72.67 64.19 to 76.91 15 Amanda is the owner of a small chain of dental offices. She sent out the yearly satisfaction survey to 600 randomly selected patients and received 544 surveys back. When looking through the results, she noticed that the downtown dental office staff had 84% of clients reporting satisfaction with services, while the uptown dental office staff had 76% of clients reporting satisfaction with services. Which of the following sets shows Amanda's null hypothesis and alternative hypothesis? Null Hypothesis: The proportion of clients satisfied at the downtown office is greater than the proportion of clients satisfied at the uptown office. Alternative Hypothesis: Downtown clients are less satisfied with the dental office staff than uptown clients. Null Hypothesis: The proportion of clients satisfied at the uptown office is 76%. Alternative Hypothesis: There is no difference in the satisfaction between the uptown and the downtown clients. Null Hypothesis: The proportion of clients satisfied at the downtown office is 84%. Alternative Hypothesis: Uptown clients are more satisfied with the dental office staff than downtown clients. Null Hypothesis: The proportion of clients satisfied at the downtown office is equal to the proportion of clients satisfied at the uptown office. Alternative Hypothesis: There is a difference in the satisfaction between the uptown and the downtown clients. 16 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Adam reads that the average speed that cars drive on the highway is 65 mph. The t-test statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. -1.39 -0.70
-1.44 -2.87 17 Sharon, an 8th grader, found the following values for weekly allowances in dollars of seven of her friends: 5, 7, 10, 8, 6, 12, and 15. If Sharon wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be? 3 8 6 7 18 Which of the following symbols represents a statistic? 19 A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are considered affluent. What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. 0.08 to 0.16 0.08 to 0.34 0.16 to 0.24 0.24 to 0.34 20 A school is gathering some data on its sports teams because it was believed that the distribution of boys and girls were evenly distributed across all the sports. This table lists the number of boys and girls participating in each sport. Boys Girls Tennis 18 30 Soccer 42 15 Swimming 12 18 Select the observed and expected frequencies for the boys participating in soccer. Observed: 57 Expected: 24
Observed: 57 Expected: 22.5 Observed: 42 Expected: 24 Observed: 42 Expected: 22.5 21 Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE? The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution The count of rolling an even number can be approximated with a normal distribution The count of rolling an odd number can be approximated with a normal distribution Rolling an even number is considered a success 22 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. He wishes to construct a 98% confidence interval. What value of t* should Adam use to construct the confidence interval? Answer choices are rounded to the thousandths place. 2.896 2.517 2.998 4.489 23 Edwin conducted a survey to find the percentage of people in an area who smoked regularly. He defined the label “smoking regularly” for males smoking 30 or more cigarettes in a day and for females smoking 20 or more. Out of 635 people who took part in the survey, 71 are labeled as people who smoke regularly. Edwin wishes to construct a significance test for his data. He finds that the proportion of chain smokers nationally is 14.1%. What is the z-statistic for this data? Answer choices are rounded to the hundredths place. -2.34
-0.24 -0.03 -2.11 24 Henri has calculated a z-test statistic of -2.73. What is the p-value of the test statistic? Answer choices are rounded to the thousandths place. 0.006 0.394 0.003 0.004 MAT 300 Unit 5 Milestone 5 Exam Answer Sophia Course What is the standard error for this set of data? 2.63 7.65 2.77 8.1 In order to get the standard error of the mean, we can use the following formula: note that s = 8.31 and n = 10 SE(mean) = Calculating Standard Error of a Sample Mean 2 Brad recorded the number of visitors at the local science museum during the week: Tuesday: 18 Wednesday: 24 Thursday: 28 Friday: 30 He expected to see 25 visitors each day. To answer whether the number of visitors follows a uniform distribution, a chi square test for goodness of fit should be performed. (alpha = 0.10) What is the chi squared test statistic? Answers are rounded to the nearest hundredth. 1.12
1.40 2.54 3.36 Using the chi-square formula we can note the test statistic is Chi-Square Test for Goodness-of-Fit 3 A school is gathering some data on its sports teams because it was believed that the distribution of boys and girls were evenly distributed across all the sports. This table lists the number of boys and girls participating in each sport. Boys Girls Tennis 18 30 Soccer 42 15 Swimming 12 18 Select the observed and expected frequencies for the boys participating in soccer. Observed: 57 Expected: 24 Observed: 42 Expected: 22.5 Observed: 42 Expected: 24 Observed: 57 Expected: 22.5 If we simply go to the chart then we can directly see the observed is 42. To find the expected frequency, we need to find the number of occurrences if the null hypothesis is true, which in this case, was that the three options are equally likely, or if the three options were all evenly distributed. First, add up all the options in the boys column: 18+42+12 = 72 If each of these three options were evenly distributed among the 72 boys, we would need to divide the total evenly between the three options: This means we would expect 24 boys to choose tennis, 24 boys to choose soccer, and 24 boys to choose swimming. Chi-Square Statistic
4 The government claims that the average age of Californians is 34 years. Joe hypothesizes that the average age of the population of California is not equal to 34 years. He records a sample mean equal to 37 and states the hypothesis as μ = 34 vs μ ≠ 34. What type of test should Joe do? Two-tailed test Right-tailed test Joe should not do any of the types of tests listed Left-tailed test Since the Ha is a not equal () sign, this indicates he wants to run a two-tailed test where the rejection region is the upper or lower tail. One-Tailed and Two-Tailed Tests 5 A researcher has a table of data with 5 column variables and 4 row variables. The value for the degrees of freedom in order to calculate the statistic is __________. 20 19 12 4 Recall to get the degrees of freedom we use df = (r-1)(c-1) where c and r are the number of rows and columns. This means df = (5-1)(4-1) = 4*3 =12. Chi-Square Test for Association and Independence 6 What do the symbols , , and represent? Variables of interest Sample statistics Population parameters Defined variables
Recall that is the population proportion, is the population standard deviation, and is the population mean. Since all these values come from the population, they are parameters. 7 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Select the 98% confidence interval for Adam’s set of data. 55.45 to 79.46 46.94 to 71.33 46.94 to 79.46 55.45 to 70.95 In order to get the 98% CI , we first need to find the critical t-score. Using a t-table, we need to find (n-1) degrees of freedom, or (8-1) = 7 df and the corresponding CI. Using the 98% CI in the bottom row and 7 df on the far left column, we get a t-critical score of 2.998. We also need to calculate the mean: So we use the formula to find the confidence interval: The lower bound is: 63.2-7.75 = 55.45 The upper bound is: 63.2+7.75 = 70.95 Confidence Intervals Using the T-Distribution 8 A table represents the number of students who passed or failed an aptitude test at two different campuses. East Campus West Campus Passed 39 45 Failed 61 55 In order to determine if there is a significant difference between campuses and pass rate, the chi square test for association and independence should be performed. What is the expected frequency of East Campus and passed? 48.3 students 39 students 42 students
50.5 students In order to get the expected counts we can note the formula is: Chi-Square Test for Homogeneity 9 Edwin conducted a survey to find the percentage of people in an area who smoked regularly. He defined the label “smoking regularly” for males smoking 30 or more cigarettes in a day and for females smoking 20 or more. Out of 635 persons who took part in the survey, 71 are labeled as people who smoke regularly. What is the standard error for the sample proportion? Answer choices are rounded to the thousandths place. 2.818 0.013 2.778 0.112 We can note the SE of the proportion is . If we note that , which means . So if we take all this information we can note SE = . Calculating Standard Error of a Sample Proportion 10 Select the statement that correctly describes a Type I error. A Type I error occurs when the null hypothesis is accepted when it is actually false. A Type I error occurs when the null hypothesis is accepted when it is actually true. A Type I error occurs when the null hypothesis is rejected when it is actually true. A Type I error occurs when the null hypothesis is rejected when it is actually false. Recall a Type I error is when we incorrectly reject a true null hypothesis. So we would reject using sample evidence, when in fact it was not true. Type I/II Errors 11
The manager of a mall conducted a survey among two groups (n1 = 100, n2 = 100) of visitors to the mall on different days. She found that the first group spent an average of 60 minutes in the mall, while the second group spent an average of 90 minutes in the mall. If the manager wishes to see the difference in the average times spent by the two groups in the mall, which of the following sets shows the null hypothesis and alternative hypothesis? Null Hypothesis: There is no difference in the average times spent by the two groups in the mall. Alternative Hypothesis: There is at least some difference in the average times spent by the two groups in the mall. Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall. Alternative Hypothesis: The difference in the average times spent by the two groups in the mall is 30 minutes. Null Hypothesis: There is no difference in the average times spent by the two groups in the mall. Alternative Hypothesis: There is a difference in the average times spent by the two groups in the mall, with a standard deviation of 30 minutes. Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall. Alternative Hypothesis: There is no difference in the average times spent by the two groups in the mall. Recall that the null hypothesis is always of no difference. So the null hypothesis (Ho) is that the mean time spent at the mall for the first group = mean time for the second group. This would indicate no difference between the two groups. The alternative hypothesis (Ha) is that there is difference in the mean time spent at the mall between the two groups. Hypothesis Testing 12 What value of z* should be used to construct an 88% confidence interval of a population mean? Answer choices are rounded to the thousandths place. 1.645 1.220 1.555 1.175
Using the z-chart to construct an 88% CI, this means that there is 6% for each tail. The lower tail would be at 0.06 and the upper tail would be at (1 - 0.06) or 0.94. The closest to 0.94 on the z-table is between 0.9394 and 0.9406. 0.9394 corresponds with a z-score of 1.55. 0.9406 corresponds with a z-score of 1.56. Taking the average of these two scores, we get a z-score of 1.555. Confidence Intervals 13 Which of the statements about one-way ANOVA is FALSE? The purpose of one way ANOVA is to verify whether the data collected from different sources converge on a common mean. It is used when there are two independent variables in the experiment. There can be any number of levels in one-way ANOVA. ANOVA deals only with one factor, such as treatment or group. When we do the one-way ANOVA we are trying to examine if the means of multiple groups are equal or not. We aren't testing independence of the variables, that is what we do with a chi-square test for independence. One-Way ANOVA/Two-Way ANOVA 14 A coin is tossed 50 times, and the number of times heads comes up is counted. Which of the following statements about the distributions of counts and proportions is FALSE? The distribution of the count of getting heads can be approximated with a normal distribution. The distribution of the count of getting tails can be approximated with a normal distribution. The count of getting heads is a binomial distribution. The count of getting heads from a sample proportion of size 20 can be approximated with a normal distribution. If we look at the counts from a large population of success and failures (2 outcomes), this is called a binomial distribution, not a normal distribution. Distribution of Sample Proportions 15
Which of the following is an example of a parameter? Half of the receipts at the coffee shop include web address for giving feedback. 9047 out of 531,310 citizens voted in the special election for city council. All of the members of the community watch group gave their availability to volunteer over the summer. 3.5% of the restaurant goers are given a survey to fill out. Recall a parameter comes from the entire set of interest, the population. Since they are looking at all members of a community here, their availability to volunteer would be an example of a parameter. Sample Statistics and Population Parameters 16 Steven measures the weight of a random sample of 49 basset hounds. The mean weight was 45.8 pounds, with a standard deviation of 3 pounds. Using the alternative hypothesis that µ < 45.8, Steven found a z test statistic of -1.5. What is the p-value of the test statistic? Answer choices are rounded to the thousandths place. 0.134 0.055 0.067 0.147 If we go to the chart and the row for the z-column for -1.5 and then the column 0, this value corresponds to 0.0668 or 0.067. How to Find a P-Value from a Z-Test Statistic 17 One condition for performing a hypothesis test is that the observations are independent. Mark is going to take a sample from a population of 400 students. How many students will Mark have to sample without replacement to treat the observations as independent? 40 300
80 360 In general we want about 10% or less to still assume independence. So size = 0.1*N = 0.1(400) = 40 A sample of 40 or less would be sufficient. Sampling With or Without Replacement 18 The data below shows the grams of fat in a series of popular snacks. If Morris wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be? 9 10 5 11 The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample size. In this case, n=10, then df = n-1 = 10-1 = 9. T-Tests 19 Edwin conducted a survey to find the percentage of people in an area who smoked regularly. He defined the label “smoking regularly” for males smoking 30 or more cigarettes in a day and for females smoking 20 or more. Out of 635 people who took part in the survey, 71 are labeled as people who smoke regularly. Edwin wishes to construct a significance test for his data. He finds that the proportion of chain smokers nationally is 14.1%. What is the z-statistic for this data? Answer choices are rounded to the hundredths place. -2.11 -2.34
-0.24 -0.03 To make things a little easier, let's first note the denominator We can now note that Finally, subbing all in we find *note that if you round, the values can be slightly different. Z-Test for Population Proportions 20 Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviation is 0.1 inch. To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be? 10 1 -1 -10 If we first note the denominator of Then, getting the z-score we can note it is This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away. Z-Test for Population Means 21 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Adam reads that the average speed that cars drive on the highway is 65 mph. The t-test statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. -0.70 -1.44 -1.39
-2.87 Using the information given, we need to find the sample mean: We now know the following information: Let's plug in the values into the formula: Calculating a T-Test Statistic 22 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. He wishes to construct a 98% confidence interval. What value of t* should Adam use to construct the confidence interval? Answer choices are rounded to the thousandths place. 4.489 2.896 2.998 2.517 Recall that we have n = 8, so the df = n-1 = 7. So if we go to the row where df = 7 and then 0.01 for the tail probability, this gives us a value of 2.998. Recall that a 98% confidence interval would have 2% for the tails, so 1% for each tail. We can also use the last row and find the corresponding confidence level. How to Find a Critical T Value 23 Edwin conducted a survey to find the percentage of people in an area who smoked regularly. He defined the label “smoking regularly” for males smoking 30 or more cigarettes in a day and for females smoking 20 or more. Out of 635 persons who took part in the survey, 71 are labeled as people who smoke regularly. What is the 90% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. 0.09 to 0.80 0.09 to 0.13 0.11 to 0.80
0.11 to 0.13 In order to get the CI we want to use the following form. First, we must determine the corresponding z*score for 90% Confidence Interval. Remember, this means that we have 5% for the tails, meaning 5%, or 0.05, for each tail. Using a z-table, we can find the upper z-score by finding (1 - 0.05) or 0.95 in the table. This corresponding z-score is at 1.645. We can know So putting it together: The lower bound is: 0.11-0.02 = 0.09 The upper bound is: 0.11 + 0.02 = 0.13 Confidence Interval for Population Proportion 24 For a left-tailed test, the critical value of z so that a hypothesis test would reject the null hypothesis at 1% significance level would be __________. Answer choices are rounded to the hundredths place. -1.28 -2.33 -1.03 -3.09 Recall that when a test statistic is smaller than in a left tailed test we would reject Ho. If we go to the standard normal chart and use 1% or 0.01, we will search for the closest value to 1% as closely as possible. 0.0099 corresponds with a z-score of -2.33. How to Find a Critical Z Value © 2019 SOPHIA Learning, LLC. SOPHIA is a registered trad