Interval Estimates Proportions Ch.8 Complete Test Bank

CHAPTER 8

TRUE/FALSE

1. As the sample size increases, the margin of error in an interval estimate of a population proportion decreases.

2. The sampling distribution of the sample proportion is the probability distribution of all possible values of the sample proportion when a sample of size n is taken from a particular population.

3. For the sampling distribution of the sample proportion, the distribution is approximately normal as long as n < 30.

4. When calculating the sample size to use in estimating a population proportion, using a proportion equal to 0.25 will provide the maximum sample size.

5. In determining a confidence interval for the difference between two population proportions, the point estimate of the difference is (–).

6. As the confidence requirement increases, the standard error term in an interval estimate of the difference between two population proportions decreases.

7. An interval estimate of a population proportion is a range of values used to estimate the population parameter .

8. A matched sample design can lead to a smaller sampling error than the independent sample design because some or all of the variation between sampled items is eliminated as a source of sampling error.

9. In a matched sample design, one uses the average for each pair of data values when building a confidence interval.

10. When each data value in one sample is paired with a corresponding data value in another sample, the samples are said to be independent.

11. One of the properties of the sampling distribution of the sample proportion is that the expected value of the sample proportion will be exactly equal to 0.5.

12. The sampling distribution of the sample mean difference is the probability distribution of all possible values of the sample mean difference when a sample of size n₁ is taken from one population and a sample of size n₂ is taken from another.

13. In any confidence interval estimate of a population proportion difference, the margin of error will be less than the standard error of the sampling distribution.

14. In a 95% confidence interval estimate of a population proportion, the margin of error will be 2.33 times the standard error of the proportion.

15. In a 95% confidence interval estimate of the difference between two population means, the standard error of the proportion will be 1.96 times the margin of error.

16.

Suppose you construct a confidence interval for the difference between two population proportions. All other things equal, the confidence interval will be narrower if the confidence level is smaller.

17.

Suppose you construct a confidence interval for a population mean difference. All other things equal, the confidence interval will be narrower if the two sample sizes are smaller.

18.

Suppose you construct a confidence interval for a population mean difference. All other things equal, the confidence interval will be narrower if the confidence level is smaller.

19.

Suppose you construct a confidence interval for the difference between two population proportions. All other things equal, the confidence interval will be wider if the two sample sizes are larger.

20.

The standard deviation of the sampling distribution of a sample proportion difference measures variation within a single sample in its response to a two-valued survey question (e.g. yes or no)

Ans FALSE; , LO: 3, Bloom: , Difficulty: Medium, Min:, AACSB:

21. The value of  that maximizes the product (1 - ) is .05.

22. In the absence of any other information, determining the largest sample size that might be necessary to build a 95% confidence interval estimate of a population proportion requires us to assume that the population proportion  is .50.

23.

To compute an interval estimate for the difference between the means of two populations when the sample sizes are small and the two population standard deviations are unknown, we can use the t distribution.

24.

When estimating the difference between two population means, the pooled sample standard deviation is appropriate whenever the two populations are assumed to have equal standard deviations.

25.

When estimating the difference between two population means, the pooled sample standard deviation is appropriate whenever the two populations are normally distributed.

26.

The sampling distribution of the sample proportion is an approximately normal distribution when n > 5 and n(1 – ) > 5.

27.

When determining the sample size for constructing a confidence interval for the difference between two population proportions, we need to know the required confidence level.

28.

When determining the sample size for constructing a confidence interval for the difference between two population proportions, we need to know the value of at least one of the two population proportions.

29. A 95% confidence interval estimate of the difference between two population proportions will contain 95% of the possible sample proportion differences.

30. For large enough sample sizes, 95% of the possible sample mean differences will be within 1.96 standard errors of the population mean difference.

MULTIPLE CHOICE

31.

In a 95% confidence interval for a population proportion,

a. the margin of error is always less than the standard error of the proportion.

b. the margin of error can be less than, equal to, or greater than the standard error of the proportion.

c. the margin of error is always greater than the standard error of the proportion.

d. the margin of error is 2.33 times greater than the standard error of the proportion.

32.

Suppose you construct a confidence interval for the difference between two population means. All other things equal, the confidence interval will be narrower if

a. the confidence level is smaller

b. the sample sizes are smaller

c. the sample means are smaller

d. the standard error of the mean difference is larger

33.

Suppose you construct a confidence interval for the difference between two population proportions. All other things equal, the confidence interval will necessarily be wider if

a. the sample sizes are larger

b. the confidence level is larger

c. the difference between the sample proportions is larger

d. the sample proportions are known

34.

The standard deviation of the sampling distribution of a sample proportion measures:

a. variation within a single sample in its response to a two-valued survey question (e.g. yes or no)

b. variation in sample proportions across samples of different sizes taken from a single population

c. variation in sample proportions across samples of a fixed size taken from different populations.

d. variation in sample proportions across different samples of a fixed size taken from a single population.

Ans D; , LO: 1, Bloom: , Difficulty: Medium, Min:, AACSB:

35.

For which of the following values of  is the value of (1 - ) maximized?

a. 1.0

b. 0.50

c. 0.75

d. 0.90

e. 0.99

36.

To compute an interval estimate for the difference between the means of two populations when the sample sizes are small and the two population standard deviations are unknown, but assumed equal, we can use

a. the t distribution

b. the standard normal distribution

c. either the t distribution or the standard normal distribution

d. the binomial distribution

e. none of the above

37.

When estimating the difference between two population means, the pooled sample standard deviation is appropriate whenever the two populations

a. are normally distributed

b. are smaller than 30

c. have equal standard deviations

d. follow a Poisson distribution

e. none of the above

38.

The sampling distribution of the sample proportion is can be treated as a normal distribution when which of the following conditions holds?

a. n > 5

b. n(1 – ) > 5

c.  has a uniform distribution

d. both a and b

e. none of the above

39.

Which of the following statements about a confidence interval when using matched samples is true?

a. it typically produces a wider interval because of the increased variation

b. it can lead to smaller sampling error than for independent samples, thus resulting in tighter intervals

c. it involves taking averages of the two values for each pair

d. all of the above

e. none of the above

40.

When determining the sample size for constructing a confidence interval for a proportion, which of the following is required?

a. target margin of error E

b. confidence requirement

c. the population proportion , or if that is not available, a sample

proportion to estimate 

d. all of the above

e. a and b only

41.

Which of the following best describes the pooled sample standard deviation under the assumption that the two population standard deviations are equal for small samples?

a. it is the square root of the weighted average of the sample variances, weighted by their respective degrees of freedom

b. it is a simple average of the sample standard deviations

c. it cannot be calculated for small samples

d. it is the square of the differences of the sample variances

e. none of the above

42.

If independent samples are taken from two normal populations and the population standard deviations are known, the sampling distribution of the difference between the two sample means

a. can be approximated by a Poisson distribution

b. will have a variance of one

c. is a normal distribution

d. will have a mean of one

e. none of the above

43.

Four economists have made economic forecasts for next year. Three forecast a downturn, one forecast an upturn.

List the 4 possible samples of size 3 that could be selected from this population of economists.

a. WXY, WXZ, WYX, XYZ

b. WXY, WXZ, WYZ, XYW

c. WZY, WXZ, WYZ, XYZ

d. WXY, WXZ, WYZ, XYZ

44.

Five consumers participate in a taste test. Two prefer beverage “A” and three prefer “B.”

List the 10 possible samples of size 3 that could be selected from this population of tasters.

a. RST, RSU, RSV, RST, RTV, RUV, STU, STV, TUV, SUV

b. RST, RSU, RSV, RTU, RTV, RUV, STU, STV, SUV, TUV

c. RST, RSU, VTV, RTU, RTV, RUV, STU, STV, TUV, UVS

d. RST, RSU, RSV, RTU, RTV, VUV, STU, STV, TUV, UVS

45.

A new golf ball design is being evaluated. A random sample of 100 pro golfers and 100 weekend golfers is given to play with for two months. After two months of regular play, the golfers in each sample were asked whether they preferred the ball they were testing to the balls they had played with previously. Seventy-eight of the pro sample said yes, while 64 of the weekend sample said yes. What are the two populations represented here?

a. Population 1: All pro golfers in the sample who prefer the new ball. Population 2: All weekend golfers in the sample who prefer the new ball.

b. Population 1: All people who play golf. Population 2: All people who do not play golf.

c. Population 1: Seventy-eight pro golfers. Population 2: Sixty-four weekend golfers.

d. Population 1: All pro golfers who would use the new ball. Population 2: All weekend golfers who would use the new ball.

46.

In a randomly selected sample of US adults, 65% said they were unsure of the new changes in health care. Suppose you construct a 95% confidence interval estimate of the proportion of all US adults who are unsure of the new changes and that the interval turns out to be .585 to .715. How should you interpret the interval?

a. We can be 95% confident that 65% of the sample are unsure.

b. 95% the US adult population, plus or minus .065, are unsure.

c. We can be 95% confident that the interval .585 to .715 contains the proportion in the sample who are unsure.

d. We can be 95% confident that the actual population proportion that is unsure will be no more than .065 away from the .65 sample proportion.

47.

You are assessing the difference in the average time that two new fully-charged solar batteries can produce electricity before they need to be again exposed to the sun. Using a sample of 50 Type 1 batteries and 50 Type 2 batteries, you build a 90% confidence interval estimate of the difference in average operating times for the two batteries and the interval turns out to be 16 plus or minus 3 hours. How should you interpret the interval?

a. We can be 90% confident that the interval 13 to 19 hours will contain the difference in average operating time for the two samples.

b. We can be 90% confident that the difference in average operating time for the two populations represented here will be 3 hours.

c. We can be 90% confident that the interval 16 plus or minus 3 hours will contain the difference in average operating time for the two populations represented here.

d. 90% of the operating times will be between 13 and 19 hours.

48.

In a simple random sample of 14 recent jobs completed by Work Crew A, the average time to complete the jobs was 22.4 hours, with a sample standard deviation of 4.7 hours. For a sample of 10 similar jobs completed by Work Crew B, the average completion time was 31.5 hours, with a standard deviation of 6.1 hours.

You plan to build a 99% confidence interval estimate of the average difference in completion times for the two populations represented here. To build the sort of interval the chapter describes, what assumptions would you need to make?

a. The two population standard deviations are equal. The two population distributions are normal.

b. The two population standard deviations are greater than 0. The two population distributions are positively skewed.

c. The two population standard deviations are greater than 5. The two population distributions are normal.

d. The two population standard deviations are normal. The means of the two population distributions are equal.

49.

A sampling plan using matched samples can be used

a. whenever both populations are non-normal.

b. to reduce the influence of “outside” factors.

c. in cases where independent samples have unequal standard deviations.

d. All of the above.

50.

Matched samples can be used to try to

a. reduce variation in sample values.

b. reduce the influence of “outside” factors.

c. produce tighter interval estimates.

d. All of the above.

51.

Before-and-after experiments in which the same subjects are observed before and after a particular treatment are a good illustration of

a. matched samples.

b. time-sensitive data.

c. non-traditional statistical methods.

d.100% sampling.

PROBLEMS

52.

Four economists have made economic forecasts for next year. Three forecast a downturn, one forecast an upturn.

Produce the 4 possible samples of size 3 that could be selected from this population of economists, determine the proportion of economists in each sample that forecast a downturn, and produce a table showing the sampling distribution of this sample proportion. Identify the proper table below.

a. Table a

b. Table b

c. Table c

d. Table d

53.

Five consumers participate in a taste test. Two prefer beverage “A” and three prefer “B.”

List the 10 possible samples of size 3 that could be selected from this population of tasters, determine the proportion of tasters in each sample who choose “A”, and then show the sampling distribution of this sample proportion in an appropriate bar chart. Choose the appropriate chart from the alternatives below.

a. Chart a

b. Chart b

c. Chart c

d. Chart d

54.

Four economists have made economic forecasts for next year. Three forecast a downturn, one forecast an upturn.

Produce the 4 possible samples of size 3 that could be selected from this population of economists, determine the proportion of economists in each sample that forecast a downturn, and produce a bar chart showing the sampling distribution of this sample proportion. Identify the proper chart below.

a. Chart a

b. Chart b

c. Chart c

d. Chart d

55.

Four economists have made economic forecasts for next year. Three forecast a downturn, one forecast an upturn.

Suppose you produce the 4 possible samples of size 3 that could be selected from this population of economists, determine the proportion of economists in each sample forecast a downturn, and produce the sampling distribution of this sample proportion. The mean (expected value) for this sampling distribution is

a. .50

b. .75

c. .675

d. .325

e. .25

56.

Four economists have made economic forecasts for next year. Three forecast a downturn, one forecast an upturn.

Suppose you produce the 4 possible samples of size 3 that could be selected from this population of economists, determine the proportion of stocks in each sample that forecast a downturn, and produce the sampling distribution of this sample proportion. The standard deviation for this sampling distribution.

a. .03

b. .34

c. .08

d. .75

e. .14

57.

Five consumers participate in a taste test. Two prefer beverage “A” and three prefer “B.”

Suppose you list the 10 possible samples of size 3 that could be selected from this population of tasters, determine the proportion of tasters in each sample that chose “A”, and then show the sampling distribution of this sample proportion. The mean (expected value) for this sampling distribution would be

a. .6

b. .525

c. .3

d. .4

e. .625

58.

Five consumers participate in a taste test. Two prefer beverage “A” and three prefer “B.”

Suppose you list the 10 possible samples of size 3 that could be selected from this population of tasters, determine the proportion of tasters in each sample that chose “A”, and then show the sampling distribution of this sample proportion. The standard deviation for this sampling distribution is

a. .15

b. .2

c. .35

d. .04

e. .09

59.

A random sample from a large population produces a sample proportion of .4. Sample size is 500. Build the 95% confidence interval estimate of the population proportion and report the upper bound for your interval.

a. .573

b. .512

c. .636

d. .443

e. .491

60.

A random sample from a large population produces a sample proportion of .3. Sample size is 400. Build a 95% confidence interval estimate of the population proportion. What is the margin of error indicated by your interval?

a. .045

b. .016

c. .080

d. .161

e. .093

61.

In a survey of 601 business owners nationwide, 74% believed that hiring would increase in the upcoming year. Build a 95% confidence interval estimate of the proportion of all business owners who believe hiring will increase during the upcoming year. Report the margin of error indicated by your interval.

a. .009

b. .213

c. .112

d. .090

e. .035

62.

In a survey of 601 business owners nationwide, 83% believed that hiring would increase in the upcoming year. Build a 95% confidence interval estimate of the proportion of all business owners who believe that hiring will increase next year. Report the margin of error indicated by your interval.

a. .08

b. ,17

c. .03

d. ,01

e. .005

63.

Forty-two of 165 randomly selected college seniors said that they had already received at least one job offer. Build a 90% confidence interval estimate of the proportion of all college seniors who already have at least one job offer. Report the margin of error indicated by your interval.

a. .103

b. .056

c. .004

d. .012

e. .002

64.

In a sample of 2500 consumer credit reports, an audit found that 780 of the reports contained at least one error. Build a 99% confidence interval estimate of the proportion of all consumer credit reports that contain at least one error. Report the margin of error indicated by your interval.

a. .056

b. .009

c. .024

d. .043

e. .093

65.

In a sample of 2500 consumer credit reports, an audit found that 780 of the reports contained at least one error. If the total number of consumer credit reports is 180 million, show the 99% confidence interval estimate of the number of credit reports that contain at least one error. Report the margin of error indicated by your interval.

a. 5,480,000

b. 4,320,000

c. 4,970,000

d. 2,360,000

e. 5,840,000

66.

You plan to build a 95% confidence interval estimate of a population proportion. You want the interval to be no wider than plus or minus .025. You expect that the population proportion will be around .35. How big a sample would be required?

a. 1398

b. 1562

c. 347

d. 1821

e. 746

67.

In the survey of 111 randomly selected CEOs in the US, 82 said they had an MBA degree. Build a 95% confidence interval estimate of the proportion of all US CEOs who have an MBA. Report the margin of error indicated by your interval.

a. .109

b. .006

c. .053

d. .082

e. .131

68.

In the survey of 111 randomly selected CEOs in the US, 82 said they had an MBA degree. Build a 95% confidence interval estimate of the proportion of all US CEOs who have an MBA. Identify the margin of error indicated by your interval.

Suppose you want to reduce the margin of error for your 95% confidence interval to plus or minus .03. How large a sample would be required? (Treat the survey of 111 CEOs as a pilot sample.)

a. 992

b. 1234

c. 678

d. 1321

e. 822

69.

According to the latest census, there are 200 million adult Americans aged 20 and over. You want to estimate the number of adult Americans in this age group who receive some form of government assistance. You plan to select a random sample and use sample results to build a 90% confidence interval. You want a sample size that will give an interval no wider plus or minus 1 million people. If a preliminary estimate of the number of adults receiving benefits is 40 million, how large a sample would you recommend?

a. 17,424

b. 21,342

c. 6,585

d. 2,123

e. 10,462

70.

You plan to build a 99% confidence interval estimate of a population proportion. You want the interval to be no wider than plus or minus .05. You have no information about the value of the population proportion. How big a sample would be appropriate?

a. 241

b. 423

c. 512

d. 666

e. 567

71.

You plan to build a 99% confidence interval estimate of a population proportion. You want the interval to be no wider than plus or minus .05. Suppose a pilot sample has given .2 as an estimate of the population proportion. Using this estimate, what would be the recommended sample size?

a. 426

b. 532

c. 660

d. 988

e. 753

72.

Quality inspectors want to build a 95% confidence interval estimate of the proportion of units in a large batch that are defective. How large a sample should they select to ensure that the 95% confidence interval is no wider than plus or minus .035? Assume the inspectors have no prior information about the likely percentage of units in the batch that are defective.

a. 321

b. 568

c. 784

d. 862

e. 204

73.

Quality inspectors want to build a 95% confidence interval estimate of the proportion of units in a large batch that are defective. How large a sample should they select to ensure that the 95% confidence interval is no wider than plus or minus .035? Assume the inspectors know from past experience with similar batches that the proportion of defectives is typically about .07.

a. 436

b. 204

c. 137

d. 356

e. 521

74.

You take a random sample of size 1500 from Population 1 and a random sample of size 1500 from Population 2. The mean of the first sample is 76; the sample standard deviation is 20. The mean of the second sample is 68; the sample standard deviation is 18. Construct the 90% confidence interval estimate of the difference between the means of the two populations represented here and report the upper bound of the interval.

a. 6.31

b. 10.78

c. 11.14

d. 5.54

e. 9.14

75.

Two Internet cable connections—call them A and B— were tested to compare download speeds. Each connection was tested 35 times. The standard deviations of the download speeds were 875 MB/sec for connection A and 1208 MB/sec for connection B. We can be 99% confident that the difference in average download speeds for the two connections is no more than 1528 MB/sec plus or minus ______ MB/sec.

a. 650

b. 775

c. 521

d. 456

e. 822

76.

You take a simple random sample of size 10 from Population 1 and a simple random sample of size 12 from Population 2. The mean of the first sample is 160; the sample standard deviation is 25. The mean of the second sample is 133; the sample standard deviation is 21. We can be 95% confident that the difference between the means of the two populations represented here is no more than 27 plus or minus ______.

a. 14.5

b. 20.4

c. 22.8

d. 16.2

e. 9.8

77.

Two Internet cable connections—call them A and B— were tested to compare download speeds. If each connection was tested 5 times, and the sample standard deviations of the download speeds were 875 MB/sec for connection A and 1208 KB/sec for connection B, build a 99% confidence interval estimate of the difference in average transfer rates. Report the upper bound for your interval. Assume the population standard deviations are the same.

a. 1012.5

b. 2214.5

c. 1652.3

d. 1357.7

e. 789.2

78.

You want to estimate the difference in the average paid sick days for public employees versus employees working in the private sector in the city. In a simple random sample of 12 public employees, the average is 12.3 days, with a standard deviation of 3.32 days. In a simple random sample of 15 private sector employees, the average is 8.4 days, with a standard deviation of 2.5 days. Build a 95% confidence interval estimate of the difference in the average number of paid sick days for the two populations represented by the samples. Report the upper bound for your interval.

a. 3.1

b. 8.9

c. 6.2

d. 4.6

e. 10.3

79.

In a random sample of 50 active stock traders, 76% said they had made money in the past 2 months. In a sample of 161 active bond traders, 61% said they had made money in the past 2 months. Build a 95% confidence interval estimate of the difference in the proportion of all traders in each of the two categories that made money in the last two months. Report the margin of error indicated by your interval.

a. .05

b. .16

c. .22

d. .19

e. .14

80.

A new golf ball design is being evaluated. A random sample of 100 pro golfers and 100 weekend golfers is given to play with for two months. After two months of regular play, the golfers in each sample were asked whether they preferred the ball they were testing to the balls they had played with previously. Seventy-eight of the pro sample said yes, while 64 of the weekend sample said yes.

Build a 90% confidence interval estimate of the difference in the proportion of golfers in the two categories who would say that they prefer the new ball. Report the upper bound for your interval.

a. .143

b. .136

c. .244

d. .189

e. .283

81.

You take a random sample of 100 recent United Airlines passengers and 100 recent Delta passengers. Eight of the United passengers and 5 of the Delta passengers report that at least one of their bags was late or lost. You build a confidence interval estimate of the difference in the proportion of United passengers and the proportion of Delta customers whose bags are lost or late. The margin of error is .05. What level of confidence could you associate with this interval?

a. about 92%

b. about 85%

c. about 67%

d. about 99%

e. about 46%

82.

Six people were randomly chosen to compare the speed of two search engines—call them engine A and engine B. The order in which each of the six people used the two search engines was randomly determined. The table below shows how long it took the members of the sample to find a similar bundle of items on each of the two search engines. Treating each searcher as a “matched pair”, and assuming that all necessary population conditions are satisfied, build a 90% confidence interval estimate of the difference in average search time for the populations represented. Report the upper bound for your interval.

Search Time in Minutes

a. 3.26

b. 2.67

c. 1,98

d. 1.23

e. 4.36

83.

Five assembly workers were randomly selected to test two different assembly procedures. The order in which the procedures were assigned to each checker was random. The number of units assembled in an 8-hour shift was recorded for each worker using each assembly procedure. Results are shown in the table below. Assuming that all necessary conditions are satisfied, build a 99% confidence interval estimate of the difference in average number of units assembled for the populations represented. Report the upper bound for your interval.

Units Assembled

a. 82.3

b. 78.2

c. 89.1

d. 99.26

e. 92.3

84.

Consider a population consisting of your four Facebook friends. Names and genders are shown below.

Using sampling without replacement, show all six possible samples of size two that could be selected from this population, show the proportion of friends in each sample who are male and produce a table showing the sampling distribution of the sample proportion. Select from the options below the bar chart for the sampling distribution that you produced.

a. Chart a

b. Chart b

c. Chart c

d. Chart d

85.

Consider a population consisting of your four Facebook friends. Names and genders are shown below.

Using sampling without replacement, show all six possible samples of size two that could be selected from this population, show the proportion of friends in each sample who are male and produce a table showing the sampling distribution of the sample proportion. Compute the mean (expected value) of the sampling distribution that you produced.

a. .5

b. .42

c. .6

d. .725

e. .25

86.

Consider a population consisting of your four Facebook friends. Names and genders are shown below.

Using sampling without replacement, show all six possible samples of size two that could be selected from this population, show the proportion of friends in each sample who are male and produce a table showing the sampling distribution of the sample proportion. Compute the standard deviation of the sampling distribution that you produced.

a. .962

b. .086

c. .167

d. .831

e. .289

87.

Kalber Industries received four orders this month. Three of the orders will be delivered late, one is on schedule.

Using sampling without replacement, show all six possible samples of size two that could be selected from this order population, show the proportion of orders in each sample that will be late and produce a table showing the sampling distribution of the sample proportion. Select from the options below the bar chart for the sampling distribution that you produced.

a. Chart a

b. Chart b

c. Chart c

d. Chart d

88.

Kalber Industries received four orders this month. Three of the orders will be delivered late, one is on schedule.

Using sampling without replacement, suppose you identify all six possible samples of size two that could be selected from this order population, show the proportion of orders in each sample that will be late and produce a table showing the sampling distribution of the sample proportion. Compute the mean (expected value) for the sampling distribution that you would produce.

a. .50

b. .625

c. .325

d. .75

e. .25

89.

Kalber Industries received four orders this month. Three of the orders will be delivered late, one is on schedule.

Using sampling without replacement, suppose you identify all six possible samples of size two that could be selected from this order population, show the proportion of orders in each sample that will be late and produce a table showing the sampling distribution of the sample proportion. Compute the standard deviation for the sampling distribution that you would produce.

a. .75

b. .50

c. .625

d. .25

e. .40

90.

You want to estimate the proportion of recent business school graduates who consider themselves to be risk takers. From the population of recent business school graduates, you take a simple random sample of 150. 12 in the sample consider themselves to be risk takers. Build a 95% interval estimate of the overall population proportion based on your sample findings. Report the upper bound for your interval.

a. .123

b. .102

c. .116

d. .089

e. .077

91.

You want to estimate the proportion of recent business school graduates who consider themselves to be risk takers. From the population of recent business school graduates, you take a simple random sample of 150. 12 in the sample consider themselves to be risk takers. Build a 99% confidence interval estimate of the population proportion based on your sample findings. Report the upper bound for your interval.

a. .121

b. .166

c. .137

d. .109

e. .101

92.

In a randomly selected sample of 200 US adults, 64% (that is, 128 sample members) said they were unsure of the new changes in health care. Construct a 95% confidence interval estimate of the proportion of all US adults who are unsure of the new health care changes. Report the upper bound for your interval.

a. .707

b. .623

c. .782

d. .663

e. .841

93.

In a randomly selected sample of 200 US adults, 64% (that is, 128 sample members) said they were unsure of the new changes in health care. Suppose you construct a 95% confidence interval estimate of the proportion of all US adults who are unsure of the new changes. How would you interpret the resulting interval?

a. We can be 95% confident that 64% of the sample are unsure.

b. 95% the US adult population, plus or minus .067, are unsure.

c. We can be 95% confident that the interval .64 plus or minus .067 contains the proportion in the sample who are unsure.

d. We can be 95% confident that the actual population proportion that is unsure will be no more than .067 away from the .64 sample proportion.

94.

In a random sample of 5,000 recent government contracts, 19.3 percent of the contracts involved cost overruns. Build a 99% confidence interval estimate of all recent government contracts that involve cost overruns. Report the upper bound for your interval.

a. .123

b. .087

c. .235

d. .199

e. .146

95.

In a random sample of 1500 students enrolled in for-profit online colleges, 810 were receiving government support for at least some of their tuition. Use this sample result to construct the 95% confidence interval estimate of the percentage of students enrolled in for-profit online colleges. Report the margin of error indicated by your interval.

a. .178

b. .025

c. .223

d. .096

e. .051

96.

You are planning to estimate the proportion of all online adults who have downloaded at least one song from iTunes during the past month. If you intend to produce a 95% confidence interval that will be no wider than plus or minus 4 percentage points (that is, plus or minus .04), how large a simple random sample would you recommend? The results of a small pilot study showed a sample proportion of .12.

a. 173

b. 254

c. 389

d. 158

e. 464

97.

You are planning to estimate the proportion of all online adults who have downloaded at least one song from iTunes during the past month. If you intend to produce a 90% confidence interval that will be no wider than plus or minus 4 percentage points (that is, plus or minus .04), how large a simple random sample would you recommend? The results of a small pilot study showed a sample proportion of .12.

a. 86

b. 406

c. 77

d. 180

e. 263

98.

You are planning to estimate the proportion of all online adults who have downloaded at least one song from iTunes during the past month. If you intend to produce a 95% confidence interval that will be no wider than plus or minus 4 percentage points (that is, plus or minus .04), how large a simple random sample would you recommend? No pilot study results are available.

a. 489

b. 600

c. 522

d. 697

e. 734

99.

You are planning to estimate the proportion of all online adults who have downloaded at least one song from iTunes during the past month. If you intend to produce a 90% confidence interval that will be no wider than plus or minus 4 percentage points (that is, plus or minus .04), how large a simple random sample would you recommend? No pilot study results are available.

a. 732

b. 426

c. 623

d. 365

e. 548

100.

You want to estimate the proportion of households in the Portland area that have no landline telephone service. Suppose you plan to take a simple random sample of Portland households and target a margin of error no larger than plus or minus .02 for a proposed 90% confidence interval estimate. How large a sample would you recommend? (Assume you have no prior information about the likely population proportion.)

a. 1026

b. 1702

c. 3425

d. 1322

e. 2963

101.

You want to estimate the proportion of your classmates are regular users of Twitter. A random sample of 200 students is selected. 85 students in the sample report that they are regular Twitter users. Construct a 90% confidence interval estimate of the population proportion here. Report the upper bound for your interval.

a. .326

b. .483

c. .414

d. .297

e. .395

102.

You want to estimate the number of students at Jeller College (enrollment: 12,000) are regular users of Twitter. A random sample of 200 students is selected. 85 students in the sample report that they are regular Twitter users. Construct a 90% confidence interval estimate of the TOTAL NUMBER of students at Jeller who are regular Twitter users. Report the upper bound for your interval.

a. 6923

b. 4321

c. 5437

d. 4967

e. 5796

103.

You want to estimate the proportion of Nike employees at Nike’s Oregon headquarters who are former Olympic athletes. You take a simple random sample of 100 Nike employees from the 3500 Nike employees at the company’s headquarters. 12 employees in the sample are former Olympic athletes. Build a 95% confidence interval estimate of the overall proportion based on your sample findings, then consider the following:

Suppose you now want to reduce the margin of error for your estimate by 30% at the 95% confidence level. How big a sample size would be required?

a. 152

b. 163

c. 288

d. 125

e. 200

104.

You are interested in estimating the proportion of accountants who begin their career at one of the Big Four accounting firms eventually make partner at the same firm they began with. If you want your estimate to be within 4 percentage points of the actual population proportion (at the 95% confidence level), how large a sample should you select? (Assume no prior information.)

a. 521

b. 688

c. 600

d. 724

e. 537

105.

You are interested in estimating the proportion of accountants who begin their career at one of the Big Four accounting firms eventually make partner at the same firm they began with. You select a random sample of 600 accountants who began their career at a Big Four accounting firm and build a 95% confidence interval estimate that indicates a margin of error of plus or minus .04. Suppose you now you want to reduce the margin of error for your estimate to plus or minus .02, but you don't want to increase the sample size beyond 600. What confidence level would you have to settle for?

a. about 82%

b. about 26%

c. about 95%

d. about 51%

e. about 67%

106.

You are planning to construct a 90% confidence interval estimate of a population proportion. You want your estimate to have a margin of error no larger than plus or minus .03. What is the minimum required sample size if the population proportion is expected to be approximately .05?

a. 144

b. 126

c. 295

d. 327

e. 102

107.

You are planning to construct a 90% confidence interval estimate of a population proportion. You want your estimate to have a margin of error no larger than plus or minus .03. What is the minimum required sample size if the population proportion is expected to be approximately .85?

a. 244

b. 297

c. 327

d. 351

e. 386

108.

You are planning to construct a 90% confidence interval estimate of a population proportion. You want your estimate to have a margin of error no larger than plus or minus .03. What is the minimum required sample size if the population proportion is expected to be approximately .55?

a. 865

b. 624

c. 698

d. 749

e. 816

109.

You are assessing the difference in the average time that two new fully-charged solar batteries can produce electricity before they need to be again exposed to the sun. Using a sample of 50 Type 1 batteries and 50 Type 2 batteries, you find the average operating time for the Type 1 battery sample is 29.2 hours, with standard deviation of 4.5 hours. For the Type 2 battery sample, average operating time is 13.1 hours with standard deviation of 3.5 hours.

Build a 90% confidence interval to estimate the difference in average operating times for the two batteries. Report the upper bound (in hours) for your interval.

a. 8.97

b. 7.43

c. 6.21

d. 5.44

e. 9.73

110.

In the sample of 500 online game players at multigame.com, the average time players spent last month playing games on the site was 11.84 hours, with standard deviation of 1.23 hours. In a sample of 400 players at gamesports.com, the average time spent last month playing games on the site was 9.48 hours, with standard deviation of 2.04 hours.

Construct the appropriate 90% confidence interval estimate of the overall difference in average game playing hours for the populations represented here. Report the upper bound for your interval. (Assume the population standard deviations are equal.)

a. 2.97

b. 1.25

c. 2.55

d. 0.54

e. 1.86

111.

In a simple random sample of 14 recent jobs completed by Work Crew A, the average time to complete the jobs was 22.4 hours, with a sample standard deviation of 4.7 hours. For a sample of 10 similar jobs completed by Work Crew B, the average completion time was 31.5 hours, with a standard deviation of 6.1 hours.

Build a 99% confidence interval estimate of the average difference in completion time for the populations represented here. Report the upper bound for your interval. (Assume the population standard deviations are equal.)

a. 9.69 hours

b. 7.45 hours

c. 10.63 hours

d. 8.44 hours

e. 7.97 hours

112.

You randomly select 12 current accounting majors and 12 finance majors at Kellogg University. Students in each sample are given a test of general business knowledge. The average score for the accounting sample was 1092, with standard deviation of 29.2. The finance sample scored an average 984, with standard deviation of 31.4.

Using a 90% confidence level, construct an appropriate interval estimate of the difference in average score for the two populations represented. (Assume that the distribution scores in the two populations is normal and that the two population distributions have equal standard deviations.) Report the upper bound for your interval.

a. 129.25

b. 78.61

c. 154.3

d. 102.37

e. 99.62

113.

Two different variations of a product ad are being tested. Variation A is presented to a panel of six randomly selected consumers. Variation B is presented to another panel of six randomly selected consumers. The table below shows the number of product details that were correctly recalled by member of the two panels.

Construct the 95% confidence interval estimate of the difference between recall averages for the populations represented. Poole the sample standard deviations and use the appropriate t-score for your interval. Report the upper bound for your interval.

a. 3.85

b. 4.06

c. 3.98

d. 4.73

e. 4.92

114.

A sample of 30 corporate CEOs and 166 small business owners is selected. Members of each sample are asked to rate, on a scale of 0 to 100, the prospects for a substantial increase in business hiring over the next year. The CEO average is 68.4, with a standard deviation of 9.6; the small business owners’ average is 63.1, with a standard deviation of 12.2. Build the 90% confidence interval estimate of the difference in average ratings for the populations represented. Report the upper bound for your interval.

a. 7.7

b. 8.6

c. 8.1

d. 8.9

e. 9.6

115.

You are planning to select a sample to estimate the difference in the average hourly wage paid to production workers in Country 1 and Country 2. You want your interval estimate of the mean hourly wage difference to show a margin of error of no more than plus or minus $.10 at the 90% confidence level. Assuming you will take samples of equal size from the two populations (that is, n₁ will equal n₂), what sample sizes would be required here? A preliminary sample showed sample standard deviations of $1.23 for the Population 1 sample and $2.04 for the Population 2 sample.

a. 1621

b. 456

c. 1545

d. 2142

e. 1722

116.

You want to estimate the difference in average assembly times for two different proposed models of a ready-to-assemble home office desk that will be sold by your company. A sample of 14 people assemble model A and another sample of 14 assemble model B. The average assembly time for the model A sample is 260 minutes, with a standard deviation of 18 minutes; for the model B, the sample average is 228 minutes, with a standard deviation of 21 minutes. Build the 90% confidence interval estimate for the difference in average assembly times for the two models. Report the upper bound for your interval.

a. 43.1

b. 39.0

c. 49.7

d. 36.2

e. 44.6

117.

In a sample of 2000 power boat owners, 47% said they use their boat “at least twice a month.” In a sample of 2000 sail boat owners, 46% said they use their boat “at least twice a month.” Build a 95% confidence interval estimate of the difference in the proportion of boat owners in the two populations represented who use their boat “at least twice a month.” Report the upper bound for your interval.

a. .031

b. .058

c. .05

d. .04

e. . 2

118.

You take a simple random sample of 150 of bike shifter levers made by Granger Cycling and find that 9 are defective. For a similar sample of 150 shifter levers made by CycleMax, 15 are defective.

Construct the appropriate 95% confidence interval estimate of the overall difference in proportion defectives for the two populations represented here. Report the upper bound for your interval.

a. .10

b. .05

c. .161

d. .07

e. .082

119.

You take a sample of 200 recent SeaSkate jet-ski buyers and 200 recent AquaKing jet-ski buyers. 142 of the SeaSkate buyers and 120 of the AquaKing buyers rated their purchase ‘10 out of 10.’

Construct the 90% confidence interval estimate of the difference in proportions for the two populations represented here. Report the upper bound for your interval.

a. .204

b. .161

c. .154

d. .187

e. .149

120.

You plan to take a sample of SeaSkate jet-ski buyers and a sample of AquaKing jet-ski buyers. You intend to construct a 90% confidence interval estimate of the difference in the proportion of buyers in the two populations represented who would give their purchase a ‘10 out of 10’ rating.

If you want your 90% interval to have a margin of error no larger than plus or minus .04, and assuming sample sizes will be equal, how large a sample from each of the two populations would you recommend? (Assume a pilot study gave sample proportions of .71 for SeaSkate buyers and .60 for AquaKing buyers.)

a. 356

b. 758

c. 432

d. 593

e. 662

121.

You plan to take a sample of SeaSkate jet-ski buyers and a sample of AquaKing jet-ski buyers. You intend to construct a 90% confidence interval estimate of the difference in the proportion of buyers in the two populations represented who would give their purchase a ‘10 out of 10’ rating.

If you want your 90% interval to have a margin of error no larger than plus or minus .04, and assuming sample sizes will be equal, how large a sample from each of the two populations would you recommend? (Assume you have no prior information about the population proportions.)

a. 925

b. 1016

c. 982

d. 851

e. 1157

122.

To test the effectiveness of two different assembly procedures, a sample of five workers is chosen. After familiarizing each of the workers with the two procedures, each worker is asked to use one assembly procedure for a full work shift, then the other for one full work shift. Which procedure a worker uses first is randomly determined. The table below shows the number of assemblies completed by each of the five workers using each of the procedures. Assuming that all necessary population conditions are satisfied, use the matched sample approach to build a 95% confidence interval estimate of the average difference in output for the populations represented. Report the upper bound for your interval.

Hourly Output

a. 8.3

b. 8.7

c. 10.1

d. 9.5

e. 8.0

123.

Of the five most recent US presidents, three wrote left-handed (Ronald Reagan wrote with his right hand but is sometimes described as left-handed due to his frequent use of the left hand). The table below gives the writing hand of each president.

List the 5 possible samples of size 4 that could be selected from this population of presidents. Find the proportion of presidents in each sample that wrote left-handed and produce a table showing the sampling distribution of this sample proportion. Identify the proper table below.

a.

b.

c.

d.

124.

Of the five most recent US presidents, three wrote left-handed (Ronald Reagan wrote with his right hand but is sometimes described as left-handed due to his frequent use of the left hand). The table below gives the writing hand of each president.

Suppose you list the 5 possible samples of size 4 that could be selected from this population of presidents, find the proportion of presidents in each sample that wrote left-handed, and show the resulting sampling distribution. The mean (expected value) of this sampling distribution would be

a. 0.50

b. 0.60

c. 0.67

d. 0.75

125.

Of the five most recent US presidents, three wrote left-handed (Ronald Reagan wrote with his right hand but is often described as left-handed due to his frequent use of the left hand). The table below gives the writing hand of each president.

Suppose you list the 5 possible samples of size 4 that could be selected from this population of presidents, find the proportion of presidents in each sample that wrote left-handed, and show the resulting sampling distribution. The standard deviation of this sampling distribution would be

a. 0.0175

b. 0.060

c. 0.122

d. 0.245

126.

In the United States, 9% of adults are military veterans (Census.gov, 2013). Suppose that you take a large number of random samples of 200 adults and calculate the proportion of military veterans in each sample. What is the expected value of the resulting distribution of sample proportions?

a. 0.0004

b. 0.02

c. 0.09

d. 18 people

127.

In the United States, 9% of adults are military veterans (Census.gov, 2013). Suppose that you take a large number of random samples of 200 adults and calculate the proportion of military veterans in each sample. What is the standard deviation of the resulting distribution of sample proportions?

a. 0.00036

b. 0.019

c. 0.090

d. Not enough information is given to find the standard deviation.

128.

In the United States, 9% of adults are military veterans (Census.gov, 2013). Suppose that a random sample of 200 adults is taken, and the proportion of veterans in the sample is calculated. What is the probability that more than 10% of those sampled will be military veterans?

a. 10%

b. 19%

c. 31%

d. 69%

129.

A 2011 Pew Research Center survey of 808 adults aged 18-34 found that 39% of those surveyed lived with one or both parents (Source: Pewsocialtrends.org, 2013). Construct a 95% confidence interval for the proportion of all adults aged 18-34 who lived with one or both parents. Use it to fill in the blanks in the following sentence: “I am 95% confident that the share of adults aged 18-34 who lived with one or both parents is between _____ and _____.”

a. 35.6%, 42.3%

b. 38.94%, 39.06%

c. 0.356%, 0.423%

d. 0.3894%, 0.3906%

130.

A 2011 survey of 1,000 Chinese adults found that 34% of those surveyed (that is, 340 people) had access to the Internet from their homes (Gallup World, 2013). Use the survey results to construct a 95% confidence interval for the proportion of all Chinese adults who have home Internet access. What is the margin of error associated with the confidence interval?

a. 0.00044

b. 0.015

c. 0.025

d. 0.029

131.

A 2011 poll of 1,000 adults in Haiti found that 9% of those surveyed (that is, 90 people) had access to the Internet from their homes (Gallup World, 2013). Use the survey results to construct a 90% confidence interval for the proportion of all Haitian adults who have home Internet access. Use it to fill in the blanks in the following sentence: “I am 90% confident that the share of Haitian adults that have home Internet access is between _____ and _____.”

a. 4.0%, 13.0%

b. 7.2%, 10.8%

c. 7.5%, 10.5%

d. 8.99%, 9.01%

132.

The population of Haiti is estimated at 10 million people. A 2011 poll of 1,000 Haitian people found that 9% of those surveyed (that is, 90 people) had access to the Internet from their homes. Use the survey results to construct a 95% confidence interval for the proportion of all Haitian adults who have home Internet access. Based on this interval, fill in the blanks in the following sentence: “I am 95% confident that the number of Haitian people who have home Internet access is between _____ and _____.”

a. 400,000 and 1,300,000

b. 720,000 and 1,080,000

c. 750,000 and 1,050,000

d. 8,990,000 and 9,010,000.

133.

Estimates vary widely as to the prevalence of cheating on campus. You plan to administer an anonymous survey to estimate the proportion of students who have cheated on a test in the past year. At a 95% confidence level, you would like your estimate to have a margin of error no greater than 3%. How large a sample should you take to ensure that you achieve your target margin of error?

a. 267 students

b. 757 students

c. 1068 students

d. Insufficient information is given to determine the necessary sample size.

134.

A 2011 survey estimated that 84% of South Africans did not have Internet access at home (Gallup World, 2011). You plan to update these survey results. To minimize costs, you want to take the smallest sample you can while remaining close to your desired margin of error. At a 95% confidence level, you would like your estimate to have a margin of error of no more than 2%. Using the 2011 results as a preliminary estimate of the population proportion, how large a sample do you need you take in order to achieve a margin of error of 2% or less?

a. 14 people

b. 174 people

c. 915 people

d. 1291 people

135.

In a random sample of 100 National Football League (NFL) players, the players’ average weight was 248 pounds with a sample standard deviation of 32 pounds. In a random sample of 80 National Basketball Association (NBA) players, the players’ average weight was 221 pounds with a sample standard deviation of 27 pounds.

Use these sample results to construct a 95% confidence interval for the difference between the average weight of NFL and NBA players. Complete the following sentence: “I am 95% confident that the average weight of NFL players is between _____________________________ than the average weight of NBA players.

a. 10.9 pounds less and 64.9 pounds greater

b. 18.4 pounds greater and 35.6 pounds greater

c. 19.7 pounds greater and 34.3 pounds greater

d. 25.4 pounds greater and 28.6 pounds greater

136.

Greg would like to test whether his running pace differs between the morning and the afternoon. In a sample of 10 morning runs, his average pace was 7 minutes 50 seconds per mile (490 seconds/mile), with a sample standard deviation of 35 seconds per mile. In a sample of 12 afternoon runs, his average pace was 7 minutes, 30 seconds per mile (450 seconds/mile), with a sample standard deviation of 32 seconds per mile.

Use the information above to construct a 95% confidence interval for the difference between Greg’s morning and afternoon pace. Assume that the population standard deviations are equal. Complete the following sentence: “I am 95% confident that Greg’s afternoon pace is between ________________ faster than his morning pace.”

a. 10.2 seconds/mile and 69.8 seconds/mile

b. 12.0 seconds/mile and 68.0 seconds/mile

c. 15.3 seconds/mile and 64.7 seconds/mile

d. 34.8 seconds/mile and 45.2 seconds/mile

137.

A 2011 survey of US adults found that in a random sample of 1,000 adults, 800 had home internet access. A corresponding survey in Canada found that of 1,000 Canadian adults, 870 had home internet access (Gallup World, 2013). Use the results of the two surveys to construct a 95% confidence interval for the difference between the proportions of US and Canadian adults with home internet access. Choose the sentence below that best summarizes your findings.

a. I am 95% confident that the share of Canadian adults with home internet access is between 3.8 and 10.2 percentage points greater than the corresponding share of US adults.

b. I am 95% confident that the share of Canadian adults with home internet access is between 4.3 and 9.7 percentage points greater than the corresponding share of US adults.

c. I am 95% confident that the share of Canadian adults with home internet access is between 6.9 and 7.1 percentage points greater than the corresponding share of US adults.

d. I am 95% confident that the share of US adults with home internet access is between 4.3 and 9.7 percentage points greater than the corresponding share of Canadian adults.

138.

A Seattle Times poll of 503 voters found that 30% of those surveyed favored the incumbent mayor in Seattle’s upcoming mayoral election. Using a 95% confidence level, the margin of error for the poll result was reported to be 4.5% (Seattle Times, September 2013). Choose the best interpretation of this poll result.

a. The share of the sample that favors the incumbent mayor is between 25.5% and 34.5%, with 95% confidence.

b. The share of voters that favors the incumbent mayor is between 25.5% and 34.5%, with 95% confidence.

c. There is a 95% chance that support for the mayor will be between 25.5% and 34.5% in the upcoming election.

d. There is a 95% chance that 30% of voters currently favor the mayor in the upcoming election.