Statistics for Business And Economics 12th Edition by James T. McClave – Test Bank

Statistics for Business And Economics 12th Edition by James T. McClave – Test Bank

CHAPTER 8—INTERVAL ESTIMATION

MULTIPLE CHOICE

1. In interval estimation, as the sample size becomes larger, the interval estimate

a.

becomes narrower

b.

becomes wider

c.

remains the same, since the mean is not changing

d.

gets closer to 1.96

ANS: A PTS: 1 TOP: Interval Estimation

2. In an interval estimation for a proportion of a population, the critical value of Z at 99.2% confidence is

a.

2.65

b.

2.44

c.

1.96

d.

1.645

ANS: A PTS: 1 TOP: Interval Estimation

3. The absolute value of the difference between the point estimate and the population parameter it estimates is

a.

the standard error

b.

the sampling error

c.

precision

d.

the error of confidence

ANS: B PTS: 1 TOP: Interval Estimation

4. When “S” is used to estimate “s,” the margin of error is computed by using

a.

normal distribution

b.

t distribution

c.

the mean of the sample

d.

the mean of the population

ANS: B PTS: 1 TOP: Interval Estimation

5. From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is

a.

15

b.

2

c.

3.92

d.

4

ANS: C PTS: 1 TOP: Interval Estimation

6. A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

a.

5

b.

9.8

c.

650

d.

609.8

ANS: B PTS: 1 TOP: Interval Estimation

7. In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is

a.

22

b.

23

c.

60

d.

61

ANS: C PTS: 1 TOP: Interval Estimation

8. If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is

a.

0.485

b.

1.96

c.

0.95

d.

1.645

ANS: C PTS: 1 TOP: Interval Estimation

9. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

a.

becomes larger

b.

becomes smaller

c.

stays the same

d.

None of these alternatives is correct.

ANS: B PTS: 1 TOP: Interval Estimation

10. For the interval estimation of m when s is known and the sample is large, the proper distribution to use is

a.

the normal distribution

b.

the t distribution with n degrees of freedom

c.

the t distribution with n + 1 degrees of freedom

d.

the t distribution with n + 2 degrees of freedom

ANS: A PTS: 1 TOP: Interval Estimation

11. An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

a.

confidence level

b.

interval estimate

c.

parameter value

d.

population estimate

ANS: B PTS: 1 TOP: Interval Estimation

12. The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

a.

confidence level

b.

margin of error

c.

parameter estimate

d.

interval estimate

ANS: B PTS: 1 TOP: Interval Estimation

13. If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be

a.

0.1

b.

0.95

c.

0.9

d.

0.05

ANS: C PTS: 1 TOP: Interval Estimation

14. Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation?

a.

standard distribution

b.

z distribution

c.

alpha distribution

d.

t distribution

ANS: D PTS: 1 TOP: Interval Estimation

15. In interval estimation, the t distribution is applicable only when

a.

the population has a mean of less than 30

b.

the sample standard deviation is used to estimate the population standard deviation

c.

the variance of the population is known

d.

the standard deviation of the population is known

ANS: B PTS: 1 TOP: Interval Estimation

16. In developing an interval estimate, if the population standard deviation is unknown

a.

it is impossible to develop an interval estimate

b.

the standard deviation is arrived at using the range

c.

the sample standard deviation can be used

d.

it is assumed that the population standard deviation is 1

ANS: C PTS: 1 TOP: Interval Estimation

17. In order to use the normal distribution for interval estimation of m when s is known and the sample is very small, the population

a.

must be very large

b.

must have a normal distribution

c.

can have any distribution

d.

must have a mean of at least 1

ANS: B PTS: 1 TOP: Interval Estimation

18. From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (m).

a.

The normal distribution can be used.

b.

The t distribution with 5 degrees of freedom must be used.

c.

The t distribution with 6 degrees of freedom must be used.

d.

The sample size must be increased.

ANS: D PTS: 1 TOP: Interval Estimation

19. A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of m, the proper distribution to use is the

a.

normal distribution

b.

t distribution with 200 degrees of freedom

c.

t distribution with 201 degrees of freedom

d.

t distribution with 202 degrees of freedom

ANS: A PTS: 1 TOP: Interval Estimation

20. From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of m, the proper distribution to use is the

a.

normal distribution

b.

t distribution with 25 degrees of freedom

c.

t distribution with 26 degrees of freedom

d.

t distribution with 24 degrees of freedom

ANS: D PTS: 1 TOP: Interval Estimation

21. The z value for a 97.8% confidence interval estimation is

a.

2.02

b.

1.96

c.

2.00

d.

2.29

ANS: D PTS: 1 TOP: Interval Estimation

22. The t value for a 95% confidence interval estimation with 24 degrees of freedom is

a.

1.711

b.

2.064

c.

2.492

d.

2.069

ANS: B PTS: 1 TOP: Interval Estimation

23. As the sample size increases, the margin of error

a.

increases

b.

decreases

c.

stays the same

d.

increases or decreases depending on the size of the mean

ANS: B PTS: 1 TOP: Interval Estimation

24. For which of the following values of P is the value of P(1 – P) maximized?

a.

P = 0.99

b.

P = 0.90

c.

P = 0.01

d.

P = 0.50

ANS: D PTS: 1 TOP: Interval Estimation

25. A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for m

a.

becomes narrower

b.

becomes wider

c.

does not change

d.

becomes 0.1

ANS: A PTS: 1 TOP: Interval Estimation

26. Using an a = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

a.

becomes narrower

b.

becomes wider

c.

does not change

d.

remains the same

ANS: B PTS: 1 TOP: Interval Estimation

27. The ability of an interval estimate to contain the value of the population parameter is described by the

a.

confidence level

b.

degrees of freedom

c.

precise value of the population mean m

d.

degrees of freedom minus 1

ANS: A PTS: 1 TOP: Interval Estimation

28. After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

a.

Increase the level of confidence for the interval.

b.

Decrease the sample size.

c.

Increase the sample size.

d.

Reduce the population variance.

ANS: C PTS: 1 TOP: Interval Estimation

29. If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect

a.

the size of the confidence interval to increase

b.

the size of the confidence interval to decrease

c.

the size of the confidence interval to remain the same

d.

the sample size to increase

ANS: A PTS: 1 TOP: Interval Estimation

30. In general, higher confidence levels provide

a.

wider confidence intervals

b.

narrower confidence intervals

c.

a smaller standard error

d.

unbiased estimates

ANS: A PTS: 1 TOP: Interval Estimation

31. An interval estimate is a range of values used to estimate

a.

the shape of the population’s distribution

b.

the sampling distribution

c.

a sample statistic

d.

a population parameter

ANS: D PTS: 1 TOP: Interval Estimation

32. In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?

a.

the maximum margin of error that can be tolerated

b.

the confidence level required

c.

a preliminary estimate of the true population proportion P

d.

the mean of the population

ANS: D PTS: 1 TOP: Interval Estimation

33. Whenever using the t distribution for interval estimation (when the sample size is very small), we must assume that

a.

the sample has a mean of at least 30

b.

the sampling distribution is not normal

c.

the population is approximately normal

d.

the finite population correction factor is necessary

ANS: C PTS: 1 TOP: Interval Estimation

34. A sample of 20 items from a population with an unknown s is selected in order to develop an interval estimate of m. Which of the following is not necessary?

a.

We must assume the population has a normal distribution.

b.

We must use a t distribution.

c.

Sample standard deviation must be used to estimate s.

d.

The sample must have a normal distribution.

ANS: D PTS: 1 TOP: Interval Estimation

35. A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for m is

a.

105.0 to 225.0

b.

175.0 to 185.0

c.

100.0 to 200.0

d.

170.2 to 189.8

ANS: D PTS: 1 TOP: Interval Estimation

36. It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of

a.

7.84

b.

31.36

c.

344.96

d.

1,936

ANS: A PTS: 1 TOP: Interval Estimation

37. A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is

a.

15.2 to 24.8

b.

19.200 to 20.800

c.

19.216 to 20.784

d.

21.2 to 22.8

ANS: B PTS: 1 TOP: Interval Estimation

38. When the level of confidence decreases, the margin of error

a.

stays the same

b.

becomes smaller

c.

becomes larger

d.

becomes smaller or larger, depending on the sample size

ANS: B PTS: 1 TOP: Interval Estimation

39. A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

a.

20.5 to 26.5

b.

24.4 to 25.6

c.

23.0 to 27.0

d.

20.0 to 30.0

ANS: B PTS: 1 TOP: Interval Estimation

40. A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is

a.

76.00 to 84.00

b.

77.40 to 86.60

c.

83.00 to 85.00

d.

68.00 to 100.00

ANS: C PTS: 1 TOP: Interval Estimation

41. The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is

a.

10

b.

11

c.

116

d.

117

ANS: D PTS: 1 TOP: Interval Estimation

42. It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

a.

25

b.

74

c.

189

d.

75

ANS: D PTS: 1 TOP: Interval Estimation

43. When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals

a.

n-1

b.

n

c.

29

d.

30

ANS: A PTS: 1 TOP: Interval Estimation

44. The following random sample from a population whose values were normally distributed was collected.

10

8

11

11

The 95% confidence interval for m is

a.

8.52 to 10.98

b.

7.75 to 12.25

c.

9.75 to 10.75

d.

8.00 to 10.00

ANS: B PTS: 1 TOP: Interval Estimation

45. The following random sample from a population whose values were normally distributed was collected.

10

12

18

16

The 80% confidence interval for m is

a.

12.054 to 15.946

b.

10.108 to 17.892

c.

10.321 to 17.679

d.

11.009 to 16.991

ANS: D PTS: 1 TOP: Interval Estimation

46. Which of the following best describes the form of the sampling distribution of the sample proportion?

a.

When standardized, it is exactly the standard normal distribution.

b.

When standardized, it is the t distribution.

c.

It is approximately normal as long as n 30.

d.

It is approximately normal as long as np 5 and n(1-p) 5.

ANS: D PTS: 1 TOP: Interval Estimation

47. In a random sample of 144 observations, = 0.6. The 95% confidence interval for P is

a.

0.52 to 0.68

b.

0.144 to 0.200

c.

0.60 to 0.70

d.

0.50 to 0.70

ANS: A PTS: 1 TOP: Interval Estimation

48. In a random sample of 100 observations, = 0.2. The 95.44% confidence interval for P is

a.

0.122 to 0.278

b.

0.164 to 0.236

c.

0.134 to 0.266

d.

0.120 to 0.280

ANS: D PTS: 1 TOP: Interval Estimation

49. A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate A is

a.

0.419 to 0.481

b.

0.40 to 0.50

c.

0.45 to 0.55

d.

1.645 to 1.96

ANS: A PTS: 1 TOP: Interval Estimation

50. A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

a.

110

b.

111

c.

216

d.

217

ANS: D PTS: 1 TOP: Interval Estimation

51. We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence?

a.

200

b.

100

c.

58

d.

385

ANS: D PTS: 1 TOP: Interval Estimation

52. In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

a.

0.871 to 0.929

b.

0.120 to 0.280

c.

0.765 to 0.835

d.

0.071 to 0.129

ANS: D PTS: 1 TOP: Interval Estimation

Exhibit 8-1

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours.

53. Refer to Exhibit 8-1. The standard error of the mean is

a.

7.50

b.

0.39

c.

2.00

d.

0.20

ANS: D PTS: 1 TOP: Interval Estimation

54. Refer to Exhibit 8-1. With a 0.95 probability, the margin of error is approximately

a.

0.39

b.

1.96

c.

0.20

d.

1.64

ANS: A PTS: 1 TOP: Interval Estimation

55. Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is

a.

7.04 to 110.96 hours

b.

7.36 to 10.64 hours

c.

7.80 to 10.20 hours

d.

8.61 to 9.39 hours

ANS: D PTS: 1 TOP: Interval Estimation

Exhibit 8-2

A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph.

56. Refer to Exhibit 8-2. If we are interested in determining an interval estimate for m at 96.6% confidence, the Z value to use is

a.

1.96

b.

0.483

c.

2.12

d.

1.645

ANS: C PTS: 1 TOP: Interval Estimation

57. Refer to Exhibit 8-2. The standard error of the mean is

a.

22.00

b.

96.60

c.

4.24

d.

2.00

ANS: D PTS: 1 TOP: Interval Estimation

58. Refer to Exhibit 8-2. If the confidence coefficient is reduced to 0.9, the standard error of the mean

a.

will increase

b.

will decrease

c.

remains unchanged

d.

becomes negative

ANS: C PTS: 1 TOP: Interval Estimation

59. Refer to Exhibit 8-2. The 96.6% confidence interval for m is

a.

63.00 to 67.00

b.

60.76 to 69.24

c.

61.08 to 68.92

d.

60.00 to 80.00

ANS: B PTS: 1 TOP: Interval Estimation

60. Refer to Exhibit 8-2. If the sample size was 100 (other factors remain unchanged), the interval for m would

a.

not change

b.

become narrower

c.

become wider

d.

become zero

ANS: C PTS: 1 TOP: Interval Estimation

Exhibit 8-3

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute.

61. Refer to Exhibit 8-3. The standard error of the mean equals

a.

0.001

b.

0.010

c.

0.100

d.

1.000

ANS: C PTS: 1 TOP: Interval Estimation

62. Refer to Exhibit 8-3. With a .95 probability, the sample mean will provide a margin of error of

a.

1.96

b.

0.10

c.

0.196

d.

1.64

ANS: C PTS: 1 TOP: Interval Estimation

63. Refer to Exhibit 8-3. The 95% confidence interval for the true average checkout time (in minutes) is

a.

3:00 to 5:00

b.

1.36 to 4.64

c.

1.00 to 5.00

d.

2.804 to 3.196

ANS: D PTS: 1 TOP: Interval Estimation

Exhibit 8-4

In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours.

64. Refer to Exhibit 8-4. The standard error of the mean is

a.

450

b.

81

c.

500

d.

50

ANS: D PTS: 1 TOP: Interval Estimation

65. Refer to Exhibit 8-4. At 95% confidence, the size of the margin of error is

a.

1.96

b.

50

c.

98

d.

42

ANS: C PTS: 1 TOP: Interval Estimation

66. Refer to Exhibit 8-4. If the sample mean is 1,858 KWH, the 95% confidence interval estimate of the population mean is

a.

1,760 to 1,956 KWH

b.

1,858 to 1,956 KWH

c.

1,760 to 1,858 KWH

d.

none of these alternatives is correct

ANS: A PTS: 1 TOP: Interval Estimation

Exhibit 8-5

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240.

67. Refer to Exhibit 8-5. If we want to provide a 95% confidence interval for the SAT scores, the degrees of freedom for reading the critical values of “t” statistic is

a.

60

b.

61

c.

62

d.

63

ANS: D PTS: 1 TOP: Interval Estimation

68. Refer to Exhibit 8-5. The “t” value for this interval estimation is

a.

1.96

b.

1.998

c.

1.64

d.

1.28

ANS: B PTS: 1 TOP: Interval Estimation