# Expert Answers

Question 18

A sample space consists of 46 separate events that are equally likely. What is the probability of each?

A. 1/24

B. 1/46

C. 1/32

D. 1/18

Question 19

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

A. 1/8

B. 3/8

C. 5/8

D. 6/8

Question 20

Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.

A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.

B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.

C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.

D. The first series is closer because the difference between red and black is smaller than the difference in the second series.

Question 21

Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles?

A. 0.8849

B. 0.5

C. 0.1131

D. 0.1151

Question

A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Estimate the mean number of cars per household for the population of households in this neighborhood. Give the 95% confidence interval.

A. 1.14 to 1.88

B. 1.12 to 1.88

C. 1.12 to 1.98

D. 1.14 to 1.98

Question 23

Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows:

67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62

Estimate the mean height of all female students at this college. Round your answer to the nearest tenth of an inch if necessary.

A. It is not possible to estimate the population mean from this sample data

B. 64.3 inches

C. 64.9 inches

D. 63.7 inches

Question 24

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that 33% of them had, or intended to, cheat on examinations. Find the margin of error for the 95% confidence interval.

A. 0.0432

B. 0.0434

C. 0.0425

D. 0.04

Question 25

The graph shows a measure of fitness (y) and miles walked weekly. Identify the probable cause of the correlation.

A. The correlation is coincidental.

B. There is a common underlying cause of the correlation.

C. There is no correlation between the variables.

D. Walking is a direct cause of the fitness.

Question 26

A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.

A. 28.0 to 30.0

B. 25.0 to 27.0

C. 29.0 to 31.0

D. 27.0 to 29.0

Question 27

The scatter plot and best-fit line show the relation among the data for the price of a stock (y) and employment (x) in arbitrary units. The correlation coefficient is 0.8. Predict the stock price for an employment value of 6.

A. 8.8

B. 6.2

C. 8.2

D. None of the values are correct

Question 28

Which line of the three shown in the scatter diagram below fits the data best?

A. A

B. B

C. C

D. All the lines are equally good

Question 29

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A. -0.9

B. 0.1

C. 0.5

D. 0.9

Question 30

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Use the line of best fit to predict the number of cars at time 4 after the end of classes.

A. 7.0

B. 6.0

C. 8.0

D. 3.5

Question 31

Select the best fit line on the scatter diagram below.

A. A

B. B

C. C

D. None of the lines is the line of best fit

Question 32

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 27% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.

A. 0.2323 to 0.3075

B. 0.2325 to 0.3075

C. 0.2325 to 0.3185

D. 0.2323 to 0.3185

Question 33

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A. 0.60

B. -0.97

C. 0.10

D. -0.60

Question 34

In a poll 0 voters in a certain state, 61% said that they opposed a voter ID bill that might hinder some legitimate voters from voting. The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence). Which statement is correct?

A. The reported margin of error is consistent with the sample size.

B. There is not enough information to determine whether the margin of error is consistent with the sample size.

C. The sample size is too small to achieve the stated margin of error.

D. For the given sample size, the margin of error should be smaller than stated.

Question 35

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Determine the amount of variation in the number of cars not explained by the variation time after school.

A. 55%

B. 70%

C. 30%

D. 45%

Question 36

Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of error?

A. 1.4

B. 1.6

C. 2.2

D. 2.6

Question 37

The scatter plot and best-fit line show the relation between the price per item (y) and the availability of that item (x) in arbitrary units. The correlation coefficient is -0.95. Determine the amount of variation in pricing explained by the variation in availability.

A. 5%

B. 10%

C. 95%

D. 90%

Question 38

30% of the fifth grade students in a large school district read below grade level. The distribution of sample proportions of samples of 100 students from this population is normal with a mean of 0.30 and a standard deviation of 0.045. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion that reads below grade level in the sample is 0.36. What is the probability that a second sample would be selected with a proportion less than 0.36?

A. 0.8932

B. 0.8920

C. 0.9032

D. 0.9048

Question 39

Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?

A. 0.8 standard deviations above the mean

B. 0.8 standard deviations below the mean

C. 7.3 standard deviations below the mean

D. 207 standard deviations below the mean

Question 40

Which point below would be an outlier if it were on the following graph?

A. (25, 20)

B. (5, 12)

C. (7, 5)

D. (5, 3)

A sample space consists of 46 separate events that are equally likely. What is the probability of each?

A. 1/24

B. 1/46

C. 1/32

D. 1/18

Question 19

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

A. 1/8

B. 3/8

C. 5/8

D. 6/8

Question 20

Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.

A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.

B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.

C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.

D. The first series is closer because the difference between red and black is smaller than the difference in the second series.

Question 21

Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles?

A. 0.8849

B. 0.5

C. 0.1131

D. 0.1151

Question

A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Estimate the mean number of cars per household for the population of households in this neighborhood. Give the 95% confidence interval.

A. 1.14 to 1.88

B. 1.12 to 1.88

C. 1.12 to 1.98

D. 1.14 to 1.98

Question 23

Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows:

67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62

Estimate the mean height of all female students at this college. Round your answer to the nearest tenth of an inch if necessary.

A. It is not possible to estimate the population mean from this sample data

B. 64.3 inches

C. 64.9 inches

D. 63.7 inches

Question 24

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that 33% of them had, or intended to, cheat on examinations. Find the margin of error for the 95% confidence interval.

A. 0.0432

B. 0.0434

C. 0.0425

D. 0.04

Question 25

The graph shows a measure of fitness (y) and miles walked weekly. Identify the probable cause of the correlation.

A. The correlation is coincidental.

B. There is a common underlying cause of the correlation.

C. There is no correlation between the variables.

D. Walking is a direct cause of the fitness.

Question 26

A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.

A. 28.0 to 30.0

B. 25.0 to 27.0

C. 29.0 to 31.0

D. 27.0 to 29.0

Question 27

The scatter plot and best-fit line show the relation among the data for the price of a stock (y) and employment (x) in arbitrary units. The correlation coefficient is 0.8. Predict the stock price for an employment value of 6.

A. 8.8

B. 6.2

C. 8.2

D. None of the values are correct

Question 28

Which line of the three shown in the scatter diagram below fits the data best?

A. A

B. B

C. C

D. All the lines are equally good

Question 29

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A. -0.9

B. 0.1

C. 0.5

D. 0.9

Question 30

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Use the line of best fit to predict the number of cars at time 4 after the end of classes.

A. 7.0

B. 6.0

C. 8.0

D. 3.5

Question 31

Select the best fit line on the scatter diagram below.

A. A

B. B

C. C

D. None of the lines is the line of best fit

Question 32

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 27% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.

A. 0.2323 to 0.3075

B. 0.2325 to 0.3075

C. 0.2325 to 0.3185

D. 0.2323 to 0.3185

Question 33

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A. 0.60

B. -0.97

C. 0.10

D. -0.60

Question 34

In a poll 0 voters in a certain state, 61% said that they opposed a voter ID bill that might hinder some legitimate voters from voting. The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence). Which statement is correct?

A. The reported margin of error is consistent with the sample size.

B. There is not enough information to determine whether the margin of error is consistent with the sample size.

C. The sample size is too small to achieve the stated margin of error.

D. For the given sample size, the margin of error should be smaller than stated.

Question 35

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Determine the amount of variation in the number of cars not explained by the variation time after school.

A. 55%

B. 70%

C. 30%

D. 45%

Question 36

Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of error?

A. 1.4

B. 1.6

C. 2.2

D. 2.6

Question 37

The scatter plot and best-fit line show the relation between the price per item (y) and the availability of that item (x) in arbitrary units. The correlation coefficient is -0.95. Determine the amount of variation in pricing explained by the variation in availability.

A. 5%

B. 10%

C. 95%

D. 90%

Question 38

30% of the fifth grade students in a large school district read below grade level. The distribution of sample proportions of samples of 100 students from this population is normal with a mean of 0.30 and a standard deviation of 0.045. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion that reads below grade level in the sample is 0.36. What is the probability that a second sample would be selected with a proportion less than 0.36?

A. 0.8932

B. 0.8920

C. 0.9032

D. 0.9048

Question 39

Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?

A. 0.8 standard deviations above the mean

B. 0.8 standard deviations below the mean

C. 7.3 standard deviations below the mean

D. 207 standard deviations below the mean

Question 40

Which point below would be an outlier if it were on the following graph?

A. (25, 20)

B. (5, 12)

C. (7, 5)

D. (5, 3)

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