## Statistics for Business And Economics 8th Edition By Paul Newbold – Test Bank

*Statistics for Business and Economics, 8e ***(Newbold)**

**Chapter 8 Estimation: Additional Topics**

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

A career counselor is interested in examining the salaries earned by graduate business school students at the end of the first year after graduation. In particular, the counselor is interested in seeing whether there is a difference between men and women graduates’ salaries. From a random sample of 20 men, the mean salary is found to be $42,780 with a standard deviation of $5,426. From a sample of 12 women, the mean salary is found to be $40,136 with a standard deviation of $4,383. Assume that the random sample observations are from normally distributed populations, and that the population variances are assumed to be equal.

1) What is the upper confidence limit of the 95% confidence interval for the difference between the population mean salary for men and women?

- A) $6,122.835
- B) $6,240.833
- C) $6,079.79
- D) $6,423.781

Answer: D

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Unknown Population Variances Assumed to Be Equal

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

2) What is the lower confidence limit of the 95% confidence interval for the difference between the population mean salary for men and women?

- A) -$1,135.781
- B) -$791.792
- C) -$952.833
- D) $834.835

Answer: A

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Unknown Population Variances Assumed to Be Equal

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

3) In order to construct a confidence interval estimate for the difference between two population means, independent samples are obtained from two normal populations with unknown but assumed to be equal variances. If the first sample contains 18 items and the second sample contains 14 items, which of the following distributions will be used?

- A) the
*t*distribution with 32 degrees of freedom - B) the
*t*distribution with 17 degrees of freedom - C) the
*t*distribution with 13 degrees of freedom - D) the
*t*distribution with 30 degrees of freedom

Answer: D

Difficulty: Easy

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Unknown Population Variances Assumed to Be Equal

AACSB: Reflective Thinking Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

In a recent survey of 240 teachers in Richmond, Virginia, 77.2% supported standardized national testing of elementary students. In a survey of 162 teachers in Raleigh, North Carolina, 64.2% supported national testing.

4) What is the upper confidence limit of the 99% confidence interval for the difference between the two population proportions?

- A) 0.249
- B) 0.222
- C) 0.265
- D) 0.278

Answer: A

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Population Proportions (Large Samples)

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

5) What is the lower confidence limit of the 99% confidence interval for the difference between the two population proportions?

- A) -0.011
- B) 0.036
- C) -0.036
- D) 0.011

Answer: D

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Population Proportions (Large Samples)

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

A dependent random sample from two normally distributed populations gives the following results:

*n* = 20, = 26.5, *s*2 = 3.2

6) What is the upper confidence limit of the 98% confidence interval for the difference between the population means?

- A) 29.81
- B) 327.95
- C) 20.60
- D) 28.32

Answer: D

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Dependent Samples

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

7) What is the lower confidence limit of the 98% confidence interval for the difference between the population means?

- A) 20.90
- B) 25.30
- C) 24.68
- D) 23.99

Answer: C

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Dependent Samples

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

8) Calculate the margin of error.

- A) 3.32
- B) 2.26
- C) 2.05
- D) 1.82

Answer: D

Difficulty: Easy

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Dependent Samples

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

9) Find the width of the 98% confidence interval.

- A) 5.46
- B) 3.64
- C) 0.91
- D) 0.60

Answer: B

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

10) The confidence interval for the difference between two population means that are normally distributed where the population variances are unknown but assumed to be equal rely on:

- A) the Satterthwaite’s approximation.
- B) the pooled sample variance.
- C) the estimated sample variance.
- D) the average sample variance.

Answer: B

Difficulty: Easy

AACSB: Reflective Thinking Skills

Course LO: Discuss the applications of confidence interval estimation

11) Calculate the margin of error for the given data assuming 95% confidence level:

*nx* = 250 *x* = 0.65 *ny* = 360 *y* = 0.78

- A) 0.085
- B) 1.05
- C) 0.052
- D) 0.072

Answer: D

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Population Proportions (Large Samples)

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

12) Calculate the margin of error for the given data assuming 95% confidence level:

*nx* = 200 *x* = 0.56 *ny* = 230 *y* = 0.46

- A) 0.124
- B) 0.094
- C) 0.112
- D) 0.265

Answer: B

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Known Population Variances

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

13) The pooled variance is formed by combining information from two independent samples.

If = 39, = 25, and *n*1 = *n*2 = 12 then is equal to:

- A) 31
- B) 45
- C) 30
- D) 32

Answer: D

Difficulty: Easy

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

14) A 95% confidence interval estimate for the difference between two population means, *μ*1 – *μ*2, is determined to be 62.75 < *μ*1 – *μ*2 < 68.52. Which of the following is true if the confidence level is reduced to 90%?

- A) The confidence interval becomes wider.
- B) The confidence interval remains the same.
- C) The confidence interval becomes narrower.
- D) More information is required to determine the answer.

Answer: C

Difficulty: Easy

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

Independent samples of math scores from students in the U.S. and Europe were collected from normal populations. A sample of 50 students from the U.S. had an average score of 570 while a sample of 50 European students had an average score of 540. The population standard deviations for the average scores of the US and European students are 102 and 115 respectively.

15) What is the upper confidence limit of the 95% confidence interval for the difference between the population means?

- A) 65.65
- B) 51.73
- C) 72.61
- D) 94.23

Answer: C

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Known Population Variances

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

16) What is the lower confidence limit of the 95% confidence interval for the difference between the population means?

- A) -24.82
- B) -12.61
- C) -29.21
- D) -18.24

Answer: B

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Known Population Variances

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

17) The confidence interval for the difference between two population means that are normally distributed where the population variances are unknown and are not assumed to be equal rely on the use of:

- A) the average sample variance.
- B) the estimated sample variance.
- C) Satterthwaite’s approximation.
- D) the pooled variance.

Answer: C

Difficulty: Easy

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Unknown Population Variances Not Assumed to Be Equal

AACSB: Reflective Thinking Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

For constructing a 95% confidence interval estimate for the difference between the means of two normally distributed populations, where the unknown population variances are assumed not to be equal, the summary statistics computed from two independent samples are as follows:

*n*1 = 50, 1 = 175, *s*1 = 18.5, *n*2 = 42, 2 = 158, and *s*2 = 32.4

18) What is the upper confidence limit of the 95% confidence interval for the difference between the means?

- A) 19.123
- B) 28.279
- C) 24.911
- D) 5.788

Answer: B

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Unknown Population Variances Not Assumed to Be Equal

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

19) What is the lower confidence limit of the 95% confidence interval for the difference between the means?

- A) 5.72
- B) 6.37
- C) 8.45
- D) 9.20

Answer: A

Difficulty: Moderate

Topic: Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, and Unknown Population Variances Not Assumed to Be Equal

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

*nx* = 360, *x* = 0.69, *ny* = 350, *y* = 0.76

20) What is the upper confidence limit of the 98% confidence interval for the difference in population proportions?

- A) -0.0151
- B) 0.004
- C) 0.007
- D) 0.025

Answer: C

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

21) What is the lower confidence limit of the 98% confidence interval for the difference in population proportions?

- A) -0.125
- B) 0.135
- C) -0.147
- D) 0.147

Answer: C

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

In calculating the 95% confidence interval for *μ*1 – *μ*2 the difference between the means of two normally distributed populations, the summary statistics from two independent samples are:

*nx* = 10, = 50, = 0.64, *ny* = 10, = 40, and = 1.86.

22) What is the upper confidence limit of the 95% confidence interval if the Population variances are unknown and are assumed to be equal?

- A) 11.050
- B) 11.072
- C) 12.056
- D) 10.980

Answer: A

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

23) What is the lower confidence limit of the 95% confidence interval if the Population variances are unknown and are assumed to be equal?

- A) 8.880
- B) 8.950
- C) 9.020
- D) 7.650

Answer: B

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

For calculating a 95% confidence interval for *μ*1 – *μ*2 the difference between the means of two normally distributed populations, the summary statistics from two independent samples are:

*nx* = 60, = 180, = 360, *ny* = 45, = 160, and = 900.

It is assumed that the Population variances are unknown and are equal.

24) What is the upper confidence limit of the 95% confidence interval?

- A) 29.505
- B) 30.172
- C) 10.006
- D) 22.797

Answer: A

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

25) What is the lower confidence limit of the 95% confidence interval?

- A) 29.505
- B) 11.587
- C) 10.495
- D) 22.797

Answer: C

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

26) In a random sample of 500 California residents, 350 indicated that they were home owners. In another random sample of 700 Florida residents, 455 indicated that they were home owners. What is the 99% confidence interval for the difference between the proportions?

- A) 0.05 ± 0.070
- B) 0.05 ± 0.085
- C) 0.05 ± 0.053
- D) 0.05 ± 0.045

Answer: A

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

27) Assuming unknown but equal population variances, determine the number of degrees of freedom for the following: *n*1 = 30, = 16.5; *n*2 = 45, and = 17.2.

- A) 59
- B) 73
- C) 61
- D) 55

Answer: B

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

28) To develop a confidence interval for the difference between the means of two populations which are normally distributed and have equal variances, two independent samples of sizes *n*1 and *n*2 are randomly selected from the two populations. What is the formula used to determine the number of degrees of freedom for the t distribution?

- A)
*n*1+*n*2 - B)
*n*1+*n*2- 1 - C)
*n*1+*n*2- 2 - D)
*n*1+*n*2+ 1

Answer: C

Difficulty: Easy

AACSB: Reflective Thinking Skills

Course LO: Discuss the applications of confidence interval estimation

29) If the population distribution of the differences between means of dependent samples is assumed to be normal, then a 100(1- α)% confidence interval for the difference between two means and dependent samples is given by:

- A) ±
*tn*-1, α/2 - B) ±
*tn*-1, α/2 - C) ±
*tn*-1, α/2 - D) ±
*tn*-1, α/2

Answer: D

Difficulty: Easy

AACSB: Reflective Thinking Skills

Course LO: Discuss the applications of confidence interval estimation

30) If the observed sample means are and then a 100(1- α)% confidence interval for the difference between two means, independent samples, and known population variances is given by:

- A) – ±
*z*α/2 - B) – ±
*z*α/2 - C) – ±
*z*α/2 - D) – ±
*z*α/2

Answer: B

Difficulty: Easy

AACSB: Reflective Thinking Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

A confidence interval for the difference between the means of two normally distributed populations based on the following dependent samples is desired:

Before

After

5

7

13

12

6

8

12

14

3

4

31) What is the margin of error at 95% Confidence interval?

- A) 2.76
- B) 1.62
- C) 1.25
- D) 2.00

Answer: B

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

32) What is the width of the interval?

- A) 4.86
- B) 2.56
- C) 3.24
- D) 6.48

Answer: C

Difficulty: Easy

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

33) What is the upper confidence limit of the 95% confidence interval?

- A) 0.42
- B) 1.48
- C) 0.043
- D) 0.05

Answer: A

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

34) What is the lower confidence limit of the 95% confidence interval?

- A) -2.82
- B) -3.88
- C) 2.45
- D) 3.88

Answer: A

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

A dependent random sample from two normally distributed populations gives the following results:

*n* = 20, = 27.5, and *sd* = 3.2

35) Find the margin of error for a 90% confidence interval for the difference in the means of the two populations.

- A) 2.75
- B) 2.29
- C) 1.24
- D) 1.86

Answer: C

Difficulty: Easy

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

36) Find the 95% confidence interval for the difference in the means of the two populations.

- A) 24.58 <
*μd*< 26.89 - B) 26.26 <
*μd*< 28.74 - C) 25.42 <
*μd*< 27.93 - D) 28.29 <
*μd*< 30.25

Answer: B

Difficulty: Easy

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

__THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:__

Independent random sampling from two normally distributed populations gives the following results:

*nx* = 55, = 520, σ*x* = 30, *ny* = 45, = 482, and σ*y* = 24

37) Find the margin of error for a 98% confidence interval for the difference in the means of the two populations.

- A) 8.50
- B) 19.86
- C) 15.77
- D) 12.58

Answer: D

Difficulty: Moderate

AACSB: Analytic Skills

Course LO: Discuss the applications of confidence interval estimation

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