1. In a recent poll of 1750 adults in the United States, 31% of the respondents said that now is a good time to look for a job. If the sampling method consisted of a random selection of 35 adults from each of the 50 states, identify the type of sampling method used.
A. Random Sampling
B. Convenience Sampling
C. Systematic sampling
D. Stratified sampling
2. An engineer is designing a machine to manufacture gloves and she obtains samples of hand lengths of randomly selected adult males. Identify the level of measurement of the hand lengths.
A. Nominal
B. Ordinal
C. Interval
D. Ratio
These data show the hand lengths (in millimeters) of randomly selected adult males.
173 179 207 158 196 195 214 199
3. Find the mean and median to the nearest tenth for this sample data.
A. Mean = 195.5, Median = 190.1 B. Mean = 190.1, Median = 195.5
C. Mean = 195.5, Median = 177.0 D. Mean = 190.1, Median = 177.0
4. Which of the following gives the sample standard deviation and the range of the data?
A. SD = 18.7, Range = 56 SD
B. SD = 18.7, Range = 214 Range
C. SD = 17.5, Range = 56
D. SD = 17.5, Range = 214
5. The following frequency distribution summarizes time spent on hygiene and grooming in the morning by 20 randomly chosen subjects. Estimate the mean amount of time spent on grooming and hygiene in the morning by using class midpoints for the minutes column.
A. Mean = 20.0
B. Mean = 24.5
C. Mean = 25.0
D. Mean = 29.5
6. Which one of the following describes a quantitative, continuous variable?
A. Uniform numbers for players on a team.
B. Number of players on a team.
C. Height of players on a team.
D. Number of points scored in a season by the players on a team.
7. Identify the percent of adults from the stemplot with pulse rates greater than or equal to 70.
A. 15.0% B. 37.5% C. 62.5% D.
8. Within which pulse rate group would the third quartile (Q3) fall?
A. 50−59 B. 60−69 C. 70−79 D.
Male pulse rate
Female pulse rate
9. Which distribution shape best describes the boxplot Female pulse rate?
A. Skewed right
B. Skewed left
C. Uniform
D. Normal
10. Which of the following statements is false concerning the box-and-whisker plots?
A. Male pulse rate has a larger interquartile range (IQR) than female pulse rate
B. Male pulse rate has a larger median than female pulse rate
C. Female pulse rate has a larger maximum than male pulse rate
D. Female pulse rate has a smaller Q1 than male pulse rate
11. Out of 50 randomly chosen adults age 65 or older, at least 30% had a Facebook account. What is the complement of this description?
A. Fifteen or fewer had a Facebook account.
B. Fewer than fifteen had a Facebook account.
C. Fifteen or more had a Facebook account.
D. None of the above
12. If P(A) = 0.09, which one of the following statements is true?
A. The probability of the complement of event A is 0.01
B. The probability of event A happening twice in a row (with replacement) is 0.0081.
C. A is an “unusual” event
D. For each 9 times event A happens, there are 100 times in which A doesn’t happen.
13. 13. Determine the probability of getting all 8 questions incorrect from the table so that this data set represents a legitimate probability distribution.
A. 0.055 P(all 8 incorrect) = P(0 correct)
B. 0.052 P(0 correct) = =1 - (0.051 + 0.017 + 0.124 + 0.215 + 0.132 + 0.123 + 0.121 + 0.162)
C. 0.058 P(0 correct) = 0.055
D. 0.051
14. Determine the expected number (mean) of correct answers
A. 4.858
B. 3.245
C. 5.412
D. 3.106
15. One card is randomly chosen from a standard deck of 52 cards. If the cards are drawn without replacement, what is the probability that one Ace and a face card are chosen in either order?
16. 70% of all people have brown eyes. What is the probability of randomly selecting 3 people and none of them have brown eyes?
A. 0.441 B. 0.343 C. 2.1 D.
17. Assume that random guesses are made for five multiple choice questions on an ACT test and that there are 5 choices on each question with probability of success 0.2. Find the probability that the number of correct answers is at least 3 (This problem meets all the requirements of a binomial situation.)
A. 0.058 B. 0.051 C. 0.942 D.
18. What is the z-score that corresponds to a height of 79 inches?
A. -2.50 B. 2.5 C. 1.85 D.
19. What symmetric interval about the mean will contain approximately 99.7% of the daily temperatures?
A. 47 to 91 B. 65 to 73 C. 61 to 77 D.
20. What is the probability of randomly selecting 1 male whose average height is at least 5’11’’?
A. 0.3085 B. 0.6914 C. 0.9431 D.
21. Which height is at the 55th percentile (rounded to the nearest whole number)?
A. 72 B. 70 C. 66 D.
22. What percentage of heights are between 60 inches and 72 inches?
A. 34% B. 76% C. 14% D.
23. Suppose random samples of 16 male heights are selected repeatedly from the population. What is the mean and standard deviation for the sampling distribution of sample means?
A. Mean = 69, SD = 2.5 B. Mean = 69, SD = 16
C. Mean = 69, SD = 40 D. Mean = 69, SD = 1
24. What is the probability of randomly selecting 12 males whose average height is at most 70 inches?
A. 0.8068 B. 0.1932 C. 0.4013 D.
Suppose you want to determine the average home run percentage for the Royals baseball team. You randomly select 48 players from Royals history and determine that the mean number of home runs per 100 times at bat is 7.64
25. Compute a 99% confidence interval for the mean home run percentage, given that the sample standard deviation was s = 5.61.
A. 7.64 ± 4.35
B. 7.64 ± 2.17
C. 7.64 ± 4.17
D. 7.64 ± 2.09
26. Assume the population standard deviation is estimated to be σ = 5.55. How large a sample, n, should be used to obtain a margin of error of 1 with 99% confidence?
A. 80
B. 15
C. 205
D. 157
27. Consider the situation given in Problem #26. Which of the following would produce a confidence interval with a larger margin of error?
A. Using a confidence level of 90%
B. Using a smaller estimate for σ
C. Using a smaller sample size
D. All of the above A through C
28. Which of the following statements is true?
A. The Central Limit Theorem states that a sampling distribution of means will not have the same shape as the population distribution from which it is taken.
B. The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.
C. The Central Limit Theorem states that the standard deviation of a sampling distribution of means (with n > 1) will have a larger standard deviation as the population distribution from which it is taken.
D. None of A through C are true.
29. If your population is normally distributed, which of the following statements regarding confidence intervals of population means is always false?
A. When σ is known, we use the critical value, z.
B. When n >30, we use the critical value, z.
C. When n < 30, we use the critical value, t.
D. None of A-C are always false.
30. POPT Popcorn is trying to determine the probability that the kernels of popcorn will pop. A margin of error of at most 2.5% is desired. How many kernels must be sampled to meet this requirement at the 95% confidence level if no preliminary estimate of is known?
A. 1537
B. 39
C. 784
D. 385
31. In a marketing survey, a random sample of 730 shoppers revealed that 638 remained loyal to their favorite supermarkets during the past year. Find a 95% confidence interval for the percentage of people who will remain loyal to their supermarket.
32. The US census reported that it takes workers an average of 28 minutes to drive home from work. City officials in Wichita believe that it takes workers in their city, on average, under 28 minutes to drive home from work. Which of the following gives the proper alternative hypothesis to test the claim that the average length of time for workers in Wichita to drive home from work is less than 28 minutes?
33. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 46 bears has a mean weight of 150.6 lb. Assuming that σ is known to be 102.5 lb, use a 0.01 significance level to test the claim that the population mean of all such bear weights is less than 165 lb. Compute the test statistic for this test with (H1: μ <165 lb)
A. −1.98
B. 0.95
C. 1.98
D. -0.95
34. The Pew Research Center conducted a survey of 1115 adults and found that 850 of them know what Twitter is. Use a 0.02 significance level to test the claim that less than 87% of adults know what Twitter is. Compute the P value for this test.
A. 0.0100
B. 0.0000
C. 0.0564
D. 0.0046
35. Suppose for a particular hypothesis test, = 0.06 and the P value = 0.05. Which of the following statements is false?
A. We reject the null hypothesis.
B. We fail to reject the null hyppthesis.
C. The observed result is "not unusual".
D. The computed test statistic, z, does fall in the shaded critical region of the tail in the normal curve.
36. A sample of 40 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The average height was 67.9 inches and the average pulse rate was 85.2 bpm. The linear correlation coefficient is r =0.802 and the equation of the regression line is
, where represents height. Find the best predicted pulse rate of a woman who is 70.4 in. tall.
A. 85.2 bpm
B. 83.0 bpm
C. 82.4 bpm
D. 67.9 bpm
37. A correlation coefficient of 0.94 between two quantitative variables A and B indicates that
A. As A increases, B tends to increase.
B. Changes in A cause changes in B.
C. As A increases, B tends to decrease.
D. There is a very weak association between A and B, and change in A will not affect B.
38. Of the scatterplot graphs below, which one represents the strongest, positive linear correlation?
CPI 31.5 45.6 110.4 166.7 189.4 187.6
Pizza Cost 0.24 0.43 0.98 1.24 1.35 1.32
39. Compute the least squares regression line for the cost of pizza.
A. ŷ = 0.1088x − 0.0066
B. ŷ = 0.0067x − 0.1088
C. ŷ = − 0.1088x + 0.0067
D. ŷ = 0.0067x + 0.1088
40. Calculate the correlation coefficient between the two variables.
A. 0.976
B. −0.976
C. 0.988
D. −0.988
A. Random Sampling
B. Convenience Sampling
C. Systematic sampling
D. Stratified sampling
2. An engineer is designing a machine to manufacture gloves and she obtains samples of hand lengths of randomly selected adult males. Identify the level of measurement of the hand lengths.
A. Nominal
B. Ordinal
C. Interval
D. Ratio
These data show the hand lengths (in millimeters) of randomly selected adult males.
173 179 207 158 196 195 214 199
3. Find the mean and median to the nearest tenth for this sample data.
A. Mean = 195.5, Median = 190.1 B. Mean = 190.1, Median = 195.5
C. Mean = 195.5, Median = 177.0 D. Mean = 190.1, Median = 177.0
4. Which of the following gives the sample standard deviation and the range of the data?
A. SD = 18.7, Range = 56 SD
B. SD = 18.7, Range = 214 Range
C. SD = 17.5, Range = 56
D. SD = 17.5, Range = 214
5. The following frequency distribution summarizes time spent on hygiene and grooming in the morning by 20 randomly chosen subjects. Estimate the mean amount of time spent on grooming and hygiene in the morning by using class midpoints for the minutes column.
A. Mean = 20.0
B. Mean = 24.5
C. Mean = 25.0
D. Mean = 29.5
6. Which one of the following describes a quantitative, continuous variable?
A. Uniform numbers for players on a team.
B. Number of players on a team.
C. Height of players on a team.
D. Number of points scored in a season by the players on a team.
7. Identify the percent of adults from the stemplot with pulse rates greater than or equal to 70.
A. 15.0% B. 37.5% C. 62.5% D.
8. Within which pulse rate group would the third quartile (Q3) fall?
A. 50−59 B. 60−69 C. 70−79 D.
Male pulse rate
Female pulse rate
9. Which distribution shape best describes the boxplot Female pulse rate?
A. Skewed right
B. Skewed left
C. Uniform
D. Normal
10. Which of the following statements is false concerning the box-and-whisker plots?
A. Male pulse rate has a larger interquartile range (IQR) than female pulse rate
B. Male pulse rate has a larger median than female pulse rate
C. Female pulse rate has a larger maximum than male pulse rate
D. Female pulse rate has a smaller Q1 than male pulse rate
11. Out of 50 randomly chosen adults age 65 or older, at least 30% had a Facebook account. What is the complement of this description?
A. Fifteen or fewer had a Facebook account.
B. Fewer than fifteen had a Facebook account.
C. Fifteen or more had a Facebook account.
D. None of the above
12. If P(A) = 0.09, which one of the following statements is true?
A. The probability of the complement of event A is 0.01
B. The probability of event A happening twice in a row (with replacement) is 0.0081.
C. A is an “unusual” event
D. For each 9 times event A happens, there are 100 times in which A doesn’t happen.
13. 13. Determine the probability of getting all 8 questions incorrect from the table so that this data set represents a legitimate probability distribution.
A. 0.055 P(all 8 incorrect) = P(0 correct)
B. 0.052 P(0 correct) = =1 - (0.051 + 0.017 + 0.124 + 0.215 + 0.132 + 0.123 + 0.121 + 0.162)
C. 0.058 P(0 correct) = 0.055
D. 0.051
14. Determine the expected number (mean) of correct answers
A. 4.858
B. 3.245
C. 5.412
D. 3.106
15. One card is randomly chosen from a standard deck of 52 cards. If the cards are drawn without replacement, what is the probability that one Ace and a face card are chosen in either order?
16. 70% of all people have brown eyes. What is the probability of randomly selecting 3 people and none of them have brown eyes?
A. 0.441 B. 0.343 C. 2.1 D.
17. Assume that random guesses are made for five multiple choice questions on an ACT test and that there are 5 choices on each question with probability of success 0.2. Find the probability that the number of correct answers is at least 3 (This problem meets all the requirements of a binomial situation.)
A. 0.058 B. 0.051 C. 0.942 D.
18. What is the z-score that corresponds to a height of 79 inches?
A. -2.50 B. 2.5 C. 1.85 D.
19. What symmetric interval about the mean will contain approximately 99.7% of the daily temperatures?
A. 47 to 91 B. 65 to 73 C. 61 to 77 D.
20. What is the probability of randomly selecting 1 male whose average height is at least 5’11’’?
A. 0.3085 B. 0.6914 C. 0.9431 D.
21. Which height is at the 55th percentile (rounded to the nearest whole number)?
A. 72 B. 70 C. 66 D.
22. What percentage of heights are between 60 inches and 72 inches?
A. 34% B. 76% C. 14% D.
23. Suppose random samples of 16 male heights are selected repeatedly from the population. What is the mean and standard deviation for the sampling distribution of sample means?
A. Mean = 69, SD = 2.5 B. Mean = 69, SD = 16
C. Mean = 69, SD = 40 D. Mean = 69, SD = 1
24. What is the probability of randomly selecting 12 males whose average height is at most 70 inches?
A. 0.8068 B. 0.1932 C. 0.4013 D.
Suppose you want to determine the average home run percentage for the Royals baseball team. You randomly select 48 players from Royals history and determine that the mean number of home runs per 100 times at bat is 7.64
25. Compute a 99% confidence interval for the mean home run percentage, given that the sample standard deviation was s = 5.61.
A. 7.64 ± 4.35
B. 7.64 ± 2.17
C. 7.64 ± 4.17
D. 7.64 ± 2.09
26. Assume the population standard deviation is estimated to be σ = 5.55. How large a sample, n, should be used to obtain a margin of error of 1 with 99% confidence?
A. 80
B. 15
C. 205
D. 157
27. Consider the situation given in Problem #26. Which of the following would produce a confidence interval with a larger margin of error?
A. Using a confidence level of 90%
B. Using a smaller estimate for σ
C. Using a smaller sample size
D. All of the above A through C
28. Which of the following statements is true?
A. The Central Limit Theorem states that a sampling distribution of means will not have the same shape as the population distribution from which it is taken.
B. The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.
C. The Central Limit Theorem states that the standard deviation of a sampling distribution of means (with n > 1) will have a larger standard deviation as the population distribution from which it is taken.
D. None of A through C are true.
29. If your population is normally distributed, which of the following statements regarding confidence intervals of population means is always false?
A. When σ is known, we use the critical value, z.
B. When n >30, we use the critical value, z.
C. When n < 30, we use the critical value, t.
D. None of A-C are always false.
30. POPT Popcorn is trying to determine the probability that the kernels of popcorn will pop. A margin of error of at most 2.5% is desired. How many kernels must be sampled to meet this requirement at the 95% confidence level if no preliminary estimate of is known?
A. 1537
B. 39
C. 784
D. 385
31. In a marketing survey, a random sample of 730 shoppers revealed that 638 remained loyal to their favorite supermarkets during the past year. Find a 95% confidence interval for the percentage of people who will remain loyal to their supermarket.
32. The US census reported that it takes workers an average of 28 minutes to drive home from work. City officials in Wichita believe that it takes workers in their city, on average, under 28 minutes to drive home from work. Which of the following gives the proper alternative hypothesis to test the claim that the average length of time for workers in Wichita to drive home from work is less than 28 minutes?
33. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 46 bears has a mean weight of 150.6 lb. Assuming that σ is known to be 102.5 lb, use a 0.01 significance level to test the claim that the population mean of all such bear weights is less than 165 lb. Compute the test statistic for this test with (H1: μ <165 lb)
A. −1.98
B. 0.95
C. 1.98
D. -0.95
34. The Pew Research Center conducted a survey of 1115 adults and found that 850 of them know what Twitter is. Use a 0.02 significance level to test the claim that less than 87% of adults know what Twitter is. Compute the P value for this test.
A. 0.0100
B. 0.0000
C. 0.0564
D. 0.0046
35. Suppose for a particular hypothesis test, = 0.06 and the P value = 0.05. Which of the following statements is false?
A. We reject the null hypothesis.
B. We fail to reject the null hyppthesis.
C. The observed result is "not unusual".
D. The computed test statistic, z, does fall in the shaded critical region of the tail in the normal curve.
36. A sample of 40 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The average height was 67.9 inches and the average pulse rate was 85.2 bpm. The linear correlation coefficient is r =0.802 and the equation of the regression line is
, where represents height. Find the best predicted pulse rate of a woman who is 70.4 in. tall.
A. 85.2 bpm
B. 83.0 bpm
C. 82.4 bpm
D. 67.9 bpm
37. A correlation coefficient of 0.94 between two quantitative variables A and B indicates that
A. As A increases, B tends to increase.
B. Changes in A cause changes in B.
C. As A increases, B tends to decrease.
D. There is a very weak association between A and B, and change in A will not affect B.
38. Of the scatterplot graphs below, which one represents the strongest, positive linear correlation?
CPI 31.5 45.6 110.4 166.7 189.4 187.6
Pizza Cost 0.24 0.43 0.98 1.24 1.35 1.32
39. Compute the least squares regression line for the cost of pizza.
A. ŷ = 0.1088x − 0.0066
B. ŷ = 0.0067x − 0.1088
C. ŷ = − 0.1088x + 0.0067
D. ŷ = 0.0067x + 0.1088
40. Calculate the correlation coefficient between the two variables.
A. 0.976
B. −0.976
C. 0.988
D. −0.988
