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1 Sadie is selecting two pieces of paper at random from the stack of colored paper in her closet. The stack contains several sheets of each of the standard colors: red, orange, yellow, green, blue, and violet. All of the following are possible outcomes for Sadie's selection, EXCEPT: Red, red Orange, yellow Green, violet Blue, black 2 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 -10 -1 3 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 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. 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 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. 4 A factory manufactures bolts. One of its employees, working in the quality control department, checks the first 20 bolts manufactured in a day for possible defects. This is what type of sampling? Voluntary response sampling Stratified sampling Convenience sampling Systematic sampling 5 The traffic volumes at a major intersection in New York were surveyed every day between one and four in the afternoon for a month to study the traffic patterns in the city. Which of the following types of bias affects the conclusions of the survey? Selection bias Non-response bias Response bias Deliberate bias 6 Adam tabulated the values for the average speed 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. If Adam wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be? 7
8 4 9 7 Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043. Keith reads that the mean nap is 22 minutes. The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. 1.43 1.39 2.88 0.70 8 A data set has its first and third quartiles as 9 and 17, respectively. Which of the following data points would be considered an outlier for the data set? 27 3 41 17 9 Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A rat weighs 3.5 pounds and costs $4.50 per week to feed, while a Beagle weighs 30 pounds and costs $9.20 per week to feed. Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth. $5.64 / lb. $0.31 / lb. $0.18 / lb. $1.60 / lb. 10 Researchers want to test the effects of a new weight loss program. They believe that gender is a significant factor. The participants are divided by gender. Then, within each group, participants are randomly assigned to either the treatment or control group.
Which of the following would be the most effective to test the effects of the new weight loss program? A matched-pair design experiment A longitudinal observational study A completely randomized design experiment A randomized block design experiment 11 Dave drives to work. While driving the car over nine days, he observes his daily average speed and lists it in the table below. Day Average Speed (MPH) 1 45 2 62 3 44 4 70 5 59 6 66 7 54 8 63 9 67 The median speed at which Dave drove to work was __________. 63 miles per hour 59 miles per hour 58.89 miles per hour 62 miles per hour 12 Tomijia and her nine classmates took a standardized test. Their scores were: 42, 44, 56, 71, 74, 83, 89, 90, 90, 92 If Tomijia received an 89 on the test, which percentile is she in? The 60th The 70th The 80th The 90th 13 The data below shows the grams of fat for a variety of snacks. Morris wants to calculate the standard error of the sample mean for this set of data.
Snack Grams of Fat Snack 1 9 Snack 2 13 Snack 3 21 Snack 4 30 Snack 5 31 Snack 6 31 Snack 7 34 Snack 8 25 Snack 9 28 Snack 10 20 What is the standard error for this set of data? 2.63 7.65 2.77 8.1 14 Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation. Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance. The number of cars on the road The number of citizens in the United States Average mileage per vehicle Average income per household 15 Using this Venn diagram, what is the probability that event A or event B occurs? 0.23 0.77 0.11
0.66 16 Carl throws a single die twice in a row. For the first throw, Carl rolled a 2; for the second throw he rolled a 4. What is the probability of rolling a 2 and then a 4? Answer choices are in the form of a percentage, rounded to the nearest whole number. 33% 36% 3% 22% 17 At Priscilla's school, the final grade for her Calculus course is weighted as follows: Tests: 50% Quizzes: 30% Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average? 77.5% 69% 73.4% 56.1% 18 Nick just received his test back. He scored a 24 out of a possible 60 points. His teacher told him the mean score on the test was a 35, with a standard deviation of 6. What is Nick's z-score? 4.17 1.83 -4.17 -1.83 19 Which of the following data types will be continuous? The number of children younger than ten that visited a planetarium last week The number of cars in 100 households
The letter grades students received on a class quiz The total weight of apples harvested in the farm in a season 20 Paul went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards. Paul has had good luck at blackjack in the past, and he actually got three blackjacks with Kings in a row the last time he played. Because of this lucky run, Paul thinks that Kings are the luckiest card. The dealer deals the first card to him. In a split second, he can see that it is a black card, but he is unsure if it is a King. What is the probability of the card being a King, given that it is a black card? Answer choices are in a percentage format, rounded to the nearest whole number. 8% 67% 23% 50% 21 For this scatterplot, the r2 value was calculated to be 0.9382.
Which of the following set of statements is true? About 94% of the variation in daily temperature can be explained by a positive linear relationship with beach visitors. The correlation coefficient, r, is 0.880 About 94% of the variation in beach visitors can be explained by a positive linear relationship with daily temperature. The correlation coefficient, r, is 0.969. There is no strong correlation in the linear association between beach visitors and daily temperatures. The correlation coefficient, r, is 0.880 About 94% of the variation in beach visitors is explained by a negative linear relationship with daily temperatures. The correlation coefficient, r, is 0.969. 22 Jenae's study ignored the fact that only some of her coffee choices had caffeine, even though her co-workers preferred caffeinated coffee. Therefore, Jenae decided to label one type of decaffeinated coffee as having caffeine to see what would happen. As she anticipated, this coffee became more popular with her co-workers, and they claimed that the extra boost of caffeine helped them focus on their work.
The growing popularity of the decaffeinated coffee among co-workers, under the false impression that it gave them extra caffeine, is an example of ________. a case-control study a treatment group the placebo effect a control group 23 A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be __________. between 1 and 2 between -1 and -2 between 0 and -1 between 0 and 1 24 In a bolt-manufacturing factory, it is estimated that 6% of the bolts being manufactured will be defective, with a 3% margin of error. Choose the statement that correctly describes the confidence interval. The percentage of defective bolts is between 3% and 9%. The percentage of defective bolts is 6% or more. The percentage of defective bolts is between 3% and 6%. The percentage of defective bolts is 6% or less. 25 Mark noticed that the probability that a certain player hits a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Answer choices are rounded to the hundredths place. 24.75 0.91 20.67 4.55
You passed this Milestone 25 questions were answered correctly. 1 David is playing a game where he flips two coins and counts the total number of heads. The possible outcomes and probabilities are shown in the probability distribution below. What is the expected value for the number of heads from flipping two coins? 1 3 2 1.5 The expected value, also called the mean of a probability distribution, is found by adding the products of each individual outcome and its probability. We can use the following formula to calculate the expected value, E(X): Expected Value 2 Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches): ŷ = -210 + 5.6x. Shawna's dad’s height is 72 inches and he weighs 182 pounds. What is the residual of weight and height for Shawna's dad? 809.2 pounds 193.2 pounds 11.2 pounds -11.2 pounds Recall that to get the residual, we take the actual value - predicted value. So if the actual height of 72 inches and the resulting actual weight is 182 pounds, we simply need the predicted weight. Using the regression line, we can say:
The predicted weight is 193.2 pounds. So the residual is:
Residuals
3 In a poll of 300 preschoolers, 125 said they preferred chocolate ice cream, 71 said they preferred vanilla, 100 said they preferred cookies & cream, and 4 said they had never eaten ice cream. If a pie chart were to be made showing the preference for each flavor, the central angle for the chocolate ice cream sector would be __________. 124° 5° 150° 41° Recall that to get the angle for something in a pie chart we use the formula (value / total value)*360. So in this case, for chocolate (value chocolate / total value) * 360 = (125/300)*360 = 150 degrees. Bar Graphs and Pie Charts 4 Fifty people were asked whether they were left handed. Six people answered "yes." What is the relative frequency of left-handed people in this group? Answer choices are rounded to the hundredths place. 8.33 0.88 1.14 0.12 The relative frequency of a left hand is: Relative Frequency Probability/Empirical Method 5 In a survey to rate the pizzas served by a pizza parlor, 250 people rated their agreement with the statement, “The pizzas here are one of the best I’ve ever had.” The answers were put into a table. Rating Frequency Strongly Agree 27 Agree 50 Neutral 75
Disagree 54 Strongly Disagree
44
The relative frequency of people who strongly agree with the statement is __________%. 27 17.6 10.8 20 To get the relative frequency, we take the ( number / total ). So in this case for strongly agree = (number strongly agree / total) = (27/250) = 0.108 or 10.8%. Frequency Tables 6 Two sets A and B are shown in the Venn diagram below. Which statement is FALSE? Set A has 12 elements. There are a total of 25 elements shown in the Venn diagram. Set B has 10 elements. Sets A and B have 5 common elements. To get the total number of items in the Venn diagram, we add up what is in A and B and outside, which is 7+5+5+3 =20 elements, not 25 elements. The intersection, or middle section, would show the common elements, which is 5 elements. The number of elements of Set A is everything in Circle A, or 7+5 = 12 elements. The number of elements of Set B is everything in Circle B, or 5+5 = 10 elements. Venn Diagrams 7 Adam tabulated the values for the average speed 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. If Adam wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be? 4
7 8 9 The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample size. In this case, n=8, then df = n-1 = 8-1 = 7. T-Tests 8 For the data plotted in the scatterplot, the r2 value was calculated to be 0.9846. Which of the following sets of statements is true? 98.5% of the variation in yearly income is explained by a linear relationship with age. The correlation coefficient, r, is 0.992 98.5% of the variation in age is explained by a nonlinear relationship with yearly income. The correlation coefficient, r, is 0.969. 98.5% of the variation in age is explained by a linear relationship with yearly income. The correlation coefficient, r, is 0.969. 98.5% of the variation in yearly income is explained by a nonlinear relationship with age. The correlation coefficient, r, is 0.992. The coefficient of determination measures the percent of variation in the outcome, y, explained by the regression. So a value of 0.9846 tells us the regression with age, x, can explain about 98.5% of the variation in income, y. We can also note that r = . Coefficient of Determination/r^2 9 A pizza owner asked 50 customers to taste a new type of topping and found that 40 people liked its taste. Which of these is an example of descriptive statistics? 80% of the people in the city where the pizza shop is located like the taste of the pizza topping. 80% of all the pizza shop's customers like the taste of the pizza topping. 80% of the surveyed customers like the taste of the pizza topping.
80% of all people like the taste of the pizza topping. Recall a descriptive statistic is a summary figure which uses the sample information at hand. Using the sample information we know 40 of 50 people or 80% like the taste of the pizza topping. Statistics Overview 10 Jenae is able to purchase a different brand of coffee for half the price from a new supplier. She anticipated that her co-workers would object to switching to the new brand, as they were really partial to the coffee they have been drinking so far. Indeed, when offered a taste test of the old brand versus the new brand, her co-workers unanimously rejected the new brand. Jenae's boss, Steven, pointed out that this result was most likely due to the fact that the taste test was not ________. blinded replicated randomized controlled Since they didn't keep the participants unaware of what brand they were tasting, this could influence the findings. So, the rejection of the new brand was likely due to not blinding them from what brand they were drinking. Blinding 11 A table represents the number of students who passed or failed an aptitude test at two different campuses. East Campus West Campus Passed 48 37 Failed 52 63 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 West Campus and failed? 63 students 57.5 students 50 students
50.7 students In order to get the expected counts we can note the formula is: Chi-Square Test for Homogeneity 12 Which statement accurately describes the data's form, direction, and strength from the scatterplot below? Form: Linear Direction: Positive Strength: Weak Form: Linear Direction: Negative Strength: Strong Form: Linear Direction: Negative Strength: Weak Form: Linear Direction: Positive Strength: Strong If we look at the data, it looks as if a straight line captures the relationship, so the form is linear. The slope of the line is positive, so it is increasing. Finally, since the dots are closely huddled around each other in a linear fashion, it looks strong. Describing Scatterplots 13 Consider this histogram showing the number of students in grade five who have one or more pets. What is the difference in the number of students with the most and least numbers of pets? 4 10 9 2
The most number of pets is 10 and there is 1 person who has this many pets. The least number of pets is 1 and there are 5 people with 1 pet. So the difference in the number of people would be 5 -1 = 4 people. Histograms 14 John randomly selects a ball from a bag containing different colored balls. The odds in favor of his picking a red ball are 3:11. What is the probability ratio for John picking a red ball from the bag? 3/11 3/10 3/14 3/8 Recall that we can go from "A:B" odds to a probability by rewriting it as the fraction "A/ (A+B)." So odds of 3:11 is equivalent to the following probability: Odds 15 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? Joe should not do any of the types of tests listed Right-tailed test Two-tailed test Left-tailed test Since the Ha is a greater than sign, this indicates he wants to run a 1 tailed test where the rejection region is the upper or right tail. This can be called a right-tailed test. One-Tailed and Two-Tailed Tests 16 A local gym conducts a survey among the people in a mall. Which survey question would have a qualitative response?
What is the amount of weight you can bench press, in pounds? Do you exercise daily? How much do you weigh, in pounds? How many servings of fruits do you eat every day? Simply stating yes or no is simply descriptive and cannot be measured numerically or used in arithmetic, so it is qualitative. Qualitative and Quantitative Data 17 To compare the teaching methodologies of two of its eighth-grade math teachers, a school decides to compare student test scores from the two classes throughout the year. Which type of statistical study is the school conducting? Prospective observational study Retrospective observational study Matched-pair design study Meta-analysis A study which gathers data moving forward is called a prospective study. Since the data is gathered on students without controlling the setting moving forward, it is a prospective observational design. Prospective and Retrospective Studies 18 A researcher has a table of data with 5 column variables and 5 row variables. The value for the degrees of freedom in order to calculate the statistic is __________. 24 16 4 25 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)(5-1) = 4*4 =16.
Pick Your Inference Test Chi-Square Test for Homogeneity Chi-Square Test for Association and Independence 19 A scientist is comparing parts of the body. The tibia length is plotted against the body length as shown below. Using the best-fit line, approximately how long would the tibia bone be if the body length is 62 inches? 14 inches 13 inches 11 inches 12 inches To get a rough estimate of the length of the tibia when the body length is 62 inches, we go to the value of 62 on the vertical axis and then see where it falls on the best-fit line. This looks to be about 12 inches. Best-Fit Line and Regression Line 20 Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year. She finds that the proportion of people taking extended vacations nationally is 15%. The z statistic for this data is __________. 0.56 0.45 -0.56 -0.45 To make things a little easier, let's first note the denominator We can now note that Finally, subbing all in we find Z-Test for Population Proportions
21 Select the statement that accurately describes unimodal distribution. A distribution in which two distinct values are more frequent than the other values. A distribution in which the values are distributed uniformly. A distribution in which one value is more frequent than other values. A distribution in which numerous values are more frequent than other values. Recall the mode is the most frequently occurring value. If a distribution is unimodal, it simply means there is one value that occurs most frequently. Shapes of Distributions 22 Scientists want to test a new pair of running shoes. A speed test is performed with two separate groups of participants. The treatment group will wear the new pair of running shoes, while the control group will not. It is believed that age and height may affect speed. Which of the following would be most effective in controlling the confounding variables, such as age and height, in this study? A longitudinal observational study A completely randomized design experiment A matched-pair design experiment A retrospective observational study In order to control for variables that may affect the study, a matched pair design which matches as closely as possible for those variables would best control for their effects. Matched-Pair Design 23 Which of the following scatterplots shows a correlation affected by an influential point? An influential point will influence correlation that doesn't lie in the range of the other data. This graphs shows an outlier that is above the other data and lower in the x-direction.
Cautions about Correlation 24
The first quartile (Q1) value from the above box plot is __________. 40 54 65 47 Note the value for Q1 is the left edge of the box, which is 47. Five Number Summary and Boxplots 25 Which of the following is an example of a false positive? A medical test coming back positive for a disease you do have. Sending a guilty man to jail. Sending an innocent man to jail. A medical test coming back negative for a disease you don't have. Sending a man to jail, when in fact he is innocent, is a false positive. False Positives/False Negatives