1. Two samples drawn from two populations are independent if:
A) the selection of one sample from a population is not related to the selection of the
second sample from the same population
B) the selection of one sample from one population does not affect the selection of the
second sample from the second population
C) the selection of one sample from a population is related to the selection of the
second sample from the same population
D) two samples selected from the same population have no relation
2. Two samples drawn from two populations are dependent if:
A) the selection of one sample from a population is not related to the selection of the
second sample from the same population
B) the selection of one sample from one population is not related to the selection of
the second sample from the second population
C) for each data value collected from one sample there corresponds another data value
collected from the second sample and both data values are collected from the same
source
D) two samples selected from the same population have no relation
Use the following to answer questions 3-4:
The mean G.P.A (grade point average) of all male students at a college is 2.75 and the mean
G.P.A of all female students at the same college is 2.98. The standard deviations of the G.P.As
are 0.36 for the males and 0.30 for the females. Suppose we take one sample of 48 male students
and another sample of 41 female students from this college. Assume the populations are
normally distributed.
3. What is the mean, rounded to two decimal places, of the sampling distribution of the
difference between the mean G.P.As for males and females?
4. What is the standard deviation of the sampling distribution of the difference between the
mean G.P.As for males and females, rounded to four decimal places?
Chapter 10
Use the following to answer questions 5-6:
The mean weekly earnings of all female workers in a state is $710 and the mean weekly earnings
of all male workers in the same state is $760. The standard deviations of the weekly earnings are
$86 for the females and $106 for the males. Suppose we take one sample of 316 female workers
and another sample of 329 male workers from this state.
5. What is the mean of the sampling distribution of the difference between the mean weekly
earnings for females and males?
6. What is the standard deviation of the sampling distribution of the difference between the
mean weekly earnings for females and males, rounded to two decimal places?
Use the following to answer questions 7-8:
The mean job-related stress score for all corporate managers is 8.40 and the mean job-related
stress score for all college professors is 5.95. The standard deviations of the job-related stress
scores are 0.66 for the corporate managers and 0.82 for the college professors. Suppose we take
one sample of 225 corporate managers and another sample of 167 college professors.
7. What is the mean, rounded to two decimal places, of the sampling distribution of the
difference between the mean stress scores for corporate managers and college professors?
8. What is the standard deviation of the sampling distribution of the difference between the
mean stress scores for corporate managers and college professors, rounded to four
decimal places?
Chapter 10
Use the following to answer questions 9-13:
A sample of 76 female workers and another sample of 48 male workers from a state produced
mean weekly earnings of $743.50 for the females and $777.63 for the males. Suppose that the
standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males.
The null hypothesis is that the mean weekly earnings are the same for females and males, while
the alternative hypothesis is that the mean weekly earnings for females is less than the mean
weekly earnings for males.
9. Derive the corresponding 95% confidence interval, rounded to two decimal places, for
the difference between the mean weekly earnings for all female and male workers in this
state.
10. The significance level for the test is 1%. What is the critical value of z?
A) -2.58 B) -1.96 C) -2.33 D) -2.17
11. What is the value of the test statistic, rounded to three decimal places?
12. What is the p-value for this test, rounded to four decimal places?
13. Do you reject or fail to reject the null hypothesis at the 1% significance level? State your
answer as “reject” or “fail to reject”, but don’t include the quotation marks.
Chapter 10
Use the following to answer questions 14-18:
A sample of 31 male students and another sample of 33 female students from the same college
produced mean G.P.As of 2.66 for the males and 2.89 for the females. Suppose that the standard
deviations of the G.P.As are 0.71 for the males and 0.63 for the females. The null hypothesis is
that the mean G.P.A’s are the same for males and females, while the alternative hypothesis is that
the mean G.P.A for males is less than the mean G.P.A for females.
14. Derive the corresponding 99% confidence interval for the difference between the mean
G.P.As for all male and female students at this college, rounded to three decimal places.
15. The significance level for the test is 2.5%. What is the critical value of z?
A) -2.58 B) -1.96 C) -2.33 D) -1.65
16. What is the value of the test statistic, rounded to three decimal places?
17. What is the p-value for this test, rounded to four decimal places?
18. Do you reject or fail to reject the null hypothesis at the 2.5% significance level? State
your answer as “reject” or “fail to reject”, but don’t include the quotation marks.
Chapter 10
Use the following to answer questions 19-23:
A sample of 126 corporate managers and another sample of 168 college professors produced
mean job-related stress scores of 7.35 for the managers and 6.86 for the professors. Suppose that
the standard deviations of the stress scores are 1.12 for the managers and 1.82 for the professors.
The null hypothesis is that the mean stress scores are the same for corporate managers and
college professors, while the alternative hypothesis is that the mean stress score for managers is
different from the mean stress score for professors.
19. Derive the corresponding 90% confidence interval for the difference between the mean
stress scores for all corporate managers and college professors, rounded to three decimal
places.
20. The significance level for the test is 1%. What are the critical values of z?
A) -2.58 and 2.58 B) -1.96 and 1.96 C) -2.33 and 2.33 D) –3.09 and 3.09
21. What is the value of the test statistic, rounded to three decimal places?
22. What is the p-value for this test, rounded to four decimal places?
23. Do you reject or fail to reject the null hypothesis at the 1% significance level? State your
answer as “reject” or “fail to reject”, but don’t include the quotation marks.
Chapter 10
Use the following to answer questions 24-30:
A sample of 20 from a population produced a mean of 66.0 and a standard deviation of 10.0. A
sample of 25 from another population produced a mean of 58.6 and a standard deviation of 13.0.
Assume that the two populations are normally distributed and the standard deviations of the two
populations are equal.
The null hypothesis is that the two population means are equal, while the alternative hypothesis
is that the two population means are different. The significance level is 5%.
24. What is the pooled standard deviation of the two samples, rounded to three decimal
places?
25. What is the standard deviation of the sampling distribution of the difference between the
means of these two samples, rounded to three decimal places?
26. Derive the corresponding 95% confidence interval for the difference between the means
of these two populations, rounded to three decimal places.
27. What are the critical values of t for the hypothesis test?
A) -2.014 and 2.014 C) -1.681 and 1.681
B) -2.017 and 2.017 D) -1.679 and 1.679
28. What is the value of the test statistic, t, rounded to three decimal places?
29. What is the p-value for this test, rounded to four decimal places?
Chapter 10
30. Do you reject or fail to reject the null hypothesis at the 5% significance level? State
your answer as “reject” or “fail to reject”, but don’t include the quotation marks.
Use the following to answer questions 31-37:
A sample of 16 from a population produced a mean of 86.9 and a standard deviation of 14.3. A
sample of 18 from another population produced a mean of 75.4 and a standard deviation of 15.9.
Assume that the two populations are normally distributed and the standard deviations of the two
populations are equal.
The null hypothesis is that the two population means are equal, while the alternative hypothesis
is that the mean of the first population is greater than the mean of the second population. The
significance level is 1%.
31. What is the pooled standard deviation of the two samples, rounded to three decimal
places?
32. What is the standard deviation of the sampling distribution of the difference between the
means of these two samples, rounded to three decimal places?
33. Derive the corresponding 99% confidence interval for the difference between the means
of these two populations, rounded to three decimal places.
34. What is the critical value of t for the hypothesis test?
A) 2.738 B) 2.449 C) 2.441 D) 2.733
Chapter 10
35. What is the value of the test statistic, t, rounded to three decimal places?
36. What is the p-value for this test, rounded to four decimal places?
37. Do you reject or fail to reject the null hypothesis at the 1% significance level? State your
answer as “reject” or “fail to reject”, but don’t include the quotation marks.
Use the following to answer questions 38-44:
A sample of 27 from a population produced a mean of 75.8 and a standard deviation of 8.3. A
sample of 22 from another population produced a mean of 80.0 and a standard deviation of 6.3.
Assume that the two populations are normally distributed and the standard deviations of the two
populations are equal.
The null hypothesis is that the two population means are equal, while the alternative hypothesis
is that the mean of the first population is less than the mean of the second population. The
significance level is 2.5%.
38. What is the pooled standard deviation of the two samples, rounded to three decimal
places?
39. What is the standard deviation of the sampling distribution of the difference between the
means of these two samples, rounded to three decimal places?
Chapter 10
40. Derive the corresponding 90% confidence interval for the difference between the means
of these two populations, rounded to three decimal places.
41. What is the critical value of t for the hypothesis test?
A) -2.012 B) -2.009 C) -2.685 D) -1.678
42. What is the value of the test statistic, t, rounded to three decimal places?
43. What is the p-value for this test, rounded to four decimal places?
44. Do you reject or fail to reject the null hypothesis? State your answer as “reject” or “fail to
reject”, but don’t include the quotation marks.
Use the following to answer questions 45-51:
A sample of 14 from a population produced a mean of 55.1 and a standard deviation of 7. A
sample of 20 from another population produced a mean of 50.1 and a standard deviation of 10.
Assume that the two populations are normally distributed and the standard deviations of the two
populations are not equal.
The null hypothesis is that the two population means are equal, while the alternative hypothesis
is that the two population means are different. The significance level is 10%.
45. What is the number of degrees of freedom of the t distribution to make a confidence
interval for the difference between the two population means?
Chapter 10
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46. What is the standard deviation of the sampling distribution of the difference between the
means of these two samples, rounded to three decimal places?
47. Derive the corresponding 90% confidence interval for the difference between the means
of these two populations, rounded to three decimal places.
48. What are the critical values of t for the hypothesis test?
A) -2.040 and 2.040 C) -2.026 and 2.026
B) -1.696 and 1.696 D) -2.045 and 2.045
49. What is the value of the test statistic, t, rounded to three decimal places?
50. What is the p-value for this test, rounded to four decimal places?
51. Do you reject or fail to reject the null hypothesis at the 10% significance level? State your
answer as “reject” or “fail to reject”, but don’t include the quotation marks.
Use the following to answer questions 52-58:
A sample of 12 from a population produced a mean of 84.4 and a standard deviation of 16. A
sample of 16 from another population produced a mean of 71.9 and a standard deviation of 14.
Assume that the two populations are normally distributed and the standard deviations of the two
populations are not equal.
The null hypothesis is that the two population means are equal, while the alternative hypothesis
is that the mean of the first population is greater than the mean of the second population. The
significance level is 2.5%.
Chapter 10
52. What is the number of degrees of freedom of the t distribution to make a confidence
interval for the difference between the two population means?
53. What is the standard deviation of the sampling distribution of the difference between the
means of these two samples, rounded to three decimal places?
54. Derive the corresponding 99% confidence interval for the difference between the means
of these two populations, rounded to three decimal places.
55. What is the critical value of t for the hypothesis test?
A) 2.319 B) 2.311 C) 1.997 D) 2.080
56. What is the value of the test statistic, t, rounded to three decimal places?
57. What is the p-value for this test, rounded to four decimal places?
58. Do you reject or fail to reject the null hypothesis at the 2.5% significance level? State
your answer as “reject” or “fail to reject”, but don’t include the quotation marks.