Homework 5 (Chapter 11.5~12.2)
Chapter 11.5~11.6
29. Consider the following hypothesis test, H 0 :   10 vs H a :   10 . A sample of
16 provides a sample mean of 11 and sample standard deviation of 3.
a. With   0.05 , what is the rejection rule?
b. Compute the value of the test statistic t . What is your conclusion?
30. Consider the following hypothesis test, H 0 :   20 vs H a :   20 . Data from a
sample of six items are: 18, 20, 16, 19, 17, 18.
a. Compute the sample mean.
b. Compute the sample standard deviation.
c. With   0.05 , what is the rejection rule?
d. Compute the value of the test statistic t .
e. What is your conclusion?
32. Consider the following hypothesis test, H 0 :   50 vs H a :   50 . Assume a
sample of 16 items provides the following test statistics. What can you say about
the p-values in each case? What are your conclusions based on   0.05 ?
a. t  2.602. b. t  1.341 . c. t  1.960 . d. t  1.055. e. t  3.261.
35. On the average, a housewife with a husband and two children is estimated to work
55 hours or less per week on household-related activities. The hours worked
during a week for a sample of eight housewives are: 58, 52, 64, 63, 59, 62, 62,
and 55.
a. Use   0.05 to test H 0 :   55 vs H a :   55 . What is your conclusion
about the mean number of hours worked per week?
b. What can you say about the p-value?
40. Consider the following hypothesis test, H 0 : p  0.2 vs H a : p  0.2 . A sample
of 400 provided a sample proportion of p  0.175 .
a. At   0.05 , what is the rejection rule?
b. Compute the value of the test statistic z .
c. What is the p-value?
d. What is your conclusion?
41. Consider the following hypothesis test, H 0 : p  0.75 vs H a : p  0.75 . A
sample of 300 is selected. Use   0.05 . Provide the value of the test statistic
z , the p-values, and your conclusion for each of the following sample results.
a. p  0.68 . b. p  0.72 . c. p  0.70 . d. p  0.77 .
45. (data set: Students) A magazine claims that 25% of its readers are college
students. A random sample of 200 readers resulted in the data set Students. A
response of Yes indicates that the reader is a college student. Use a 0.10 level of
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significance to test H 0 : p  0.25 vs H a : p  0.25 . What is the p-value?
49. At least 20% of all workers are believed to be willing to work fewer hours for less
pay to obtain more time for personal and leisure activities. A USA
Today/CNN/Gallup poll with a sample of 596 respondents found 83 willing to
work fewer hours for less pay to obtain more personal and leisure time (USA
Today, April 10, 1995). Test H 0 : p  0.20 vs H a : p  0.20 using a 0.05 level
of significance. What is your conclusion?
Chapter 12.1~12.2
1. Consider the following results for two independent random samples taken from
two populations.
Sample 1
Sample 2
n1  50
n2  35
x1  13.6
s1  2.2 s
x2  11.6
s2  3.0
a. What is the point estimate of the difference between the two population
means?
b. Provide a 90% confidence interval for the difference between the two
population means.
c. Provide a 95% confidence interval for the difference between the two
population means.
3. Consider the following data for two independent random samples taken from two
populations.
Sample 1
Sample 2
10, 12, 7, 7, 7, 9
8, 8, 6, 7, 4, 9
a. Compute the two sample means.
b. Compute the two sample standard deviations.
c. What is the point estimate of the difference between the two population
means?
d. What is the pooled estimate of the population variance?
e. Develop a 95% confidence interval for the difference between the two
population means.
9. Women who are union members earn $2.50 per hour more than women who are not
union members (The Wall Street Journal, July 26, 1994). Suppose independent
random samples of 15 unionized women and 20 nonunionized women in
manufacturing have been selected and the following hourly wage rates are found.
Union Workers
Nonunion Workers
22.4, 18.9, 16.7, 14.05, 16.20, 20, 16.1,
16.3, 19.1, 16.5, 18.5, 19.8, 17, 14.3,
17.6, 14.4, 16.6, 15, 17.65, 15, 17.55,
13.3, 11.2, 15.9, 19.2, 11.85, 16.65, 15.2,
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17.2
15.3, 17, 15.1, 14.3, 13.9, 14.5
a. Suppose we want to develop an interval estimate of the difference in the mean
wage rates between unionized and nonunionized women working in
manufacturing. What assumptions must be made about the two populations?
b. What is the pooled estimate of the population variance?
c. Develop a 95% confidence interval for the difference between the two
population means.
d. Does there appear to be any difference in the mean wage rate between these
two groups? Explain.
10. Consider the following hypothesis test, H 0 : 1   2  0 vs H a : 1   2  0 .
The following results are for two independent samples taken from the two
populations.
Sample 1
Sample 2
n1  40
n2  50
x1  25.2
x2  22.8
s1  5.2
s2  6.0
a. With   0.05 , what is your hypothesis-testing conclusion?
b. What is the p-value?
12. Consider the following hypothesis test, H 0 : 1   2  0 vs H a : 1   2  0 .
The following results are for two independent samples taken from the two populations.
With   0.05 , what is your hypothesis-testing conclusion?
Sample 1
Sample 2
n1  8
n2  7
x1  1.4
x2  1.0
s1  0.4
s2  0.6
17. Starting annual salaries for individuals entering the public accounting and
financial planning professions were presented in Fortune, June 26, 1995. The Starting
salaries for a sample of 12 public accountants and a sample of 14 financial planners
follow, with data in thousands of dollars.
Public Accountant
Financial Planner
30.6, 31.2, 28.9, 35.2, 25.1, 33.2, 31.3,
35.3, 31, 30.1, 29.9, 24.4
31.6, 26.6, 25.5, 25, 25.9, 32.9, 26.9,
25.8, 27.5, 29.6, 23.9, 26.9, 24.4, 25.5
a. Using   0.05 , test for any difference between the population mean starting
annual salaries for the two professions. What is your conclusion?
b. What is the point estimate of the difference between the two population means?
Which profession has the higher mean annual starting salary?
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