INSTRUCTOR ANSWER GUIDE
OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
,OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
CHAPTER 12: F DISTRIBUTION AND ONE-WAY ANOVA
There are two assumptions that must be true in order to perform an F test of two
Exercise 1. variances.
Name one assumption that must be true.
Solution The populations from which the two samples are drawn are normally distributed.
Exercise 2. There are two assumptions that must be true in order to perform an F test of two
variances.
What is the other assumption that must be true?
Solution The two populations are independent of each other.
Exercise 3. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
State the null and alternative hypotheses.
Solution H0: 1 = 2; Ha: 1 < 2 or H0: σ 12=σ 22 ; H a : σ 21 <σ 22
Exercise 4. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is s1 in this problem?
Solution 3.47
Exercise 5. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
2
October 28, 2025
,OpenStax Introductory Business Statistics 2e
Instructor Answer and Solution Guide
Chapter 12: F Distribution and One-Way ANOVA
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is s2 in this problem?
Solution 4.11
Exercise 6. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is n?
Solution 20
Exercise 7. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is the F statistic?
Solution 0.7159
Exercise 9. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
Is the claim accurate?
Solution No, at the 10% level of significance, we do not reject the null hypothesis and state
that the data do not show that the variation in drive times for the first worker is less
than the variation in drive times for the second worker.
3
October 28, 2025
, OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
Exercise 10. Two students are interested in whether or not there is variation in their test scores
for math class. There are 15 total math tests they have taken so far. The first
student’s grades have a standard deviation of 38.1. The second student’s grades
have a standard deviation of 22.5. The second student thinks his scores are lower.
State the null and alternative hypotheses.
Solution
Exercise 11. Two students are interested in whether or not there is variation in their test scores
for math class. There are 15 total math tests they have taken so far. The first
student’s grades have a standard deviation of 38.1. The second student’s grades
have a standard deviation of 22.5. The second student thinks his scores are lower.
What is the F Statistic?
Solution 2.8674
Exercise 13. Two students are interested in whether or not there is variation in their test scores
for math class. There are 15 total math tests they have taken so far. The first
student’s grades have a standard deviation of 38.1. The second student’s grades
have a standard deviation of 22.5. The second student thinks his scores are lower.
At the 5% significance level, do we reject the null hypothesis?
Solution Reject the null hypothesis. There is enough evidence to say that the variance of the
grades for the first student is higher than the variance in the grades for the second
student.
Exercise 14. Two cyclists are comparing the variances of their overall paces going uphill. Each
cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of
23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their
variances are the same or different.
State the null and alternative hypotheses
Solution
Exercise 15. Two cyclists are comparing the variances of their overall paces going uphill. Each
cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of
23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their
4
October 28, 2025
OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
,OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
CHAPTER 12: F DISTRIBUTION AND ONE-WAY ANOVA
There are two assumptions that must be true in order to perform an F test of two
Exercise 1. variances.
Name one assumption that must be true.
Solution The populations from which the two samples are drawn are normally distributed.
Exercise 2. There are two assumptions that must be true in order to perform an F test of two
variances.
What is the other assumption that must be true?
Solution The two populations are independent of each other.
Exercise 3. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
State the null and alternative hypotheses.
Solution H0: 1 = 2; Ha: 1 < 2 or H0: σ 12=σ 22 ; H a : σ 21 <σ 22
Exercise 4. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is s1 in this problem?
Solution 3.47
Exercise 5. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
2
October 28, 2025
,OpenStax Introductory Business Statistics 2e
Instructor Answer and Solution Guide
Chapter 12: F Distribution and One-Way ANOVA
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is s2 in this problem?
Solution 4.11
Exercise 6. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is n?
Solution 20
Exercise 7. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
What is the F statistic?
Solution 0.7159
Exercise 9. Two coworkers commute from the same building. They are interested in whether or
not there is any variation in the time it takes them to drive to work. They each record
their times for 20 commutes. The first worker’s times have a variance of 12.1. The
second worker’s times have a variance of 16.9. The first worker thinks that he is
more consistent with his commute times and that his commute time is shorter. Test
the claim at the 10% level.
Is the claim accurate?
Solution No, at the 10% level of significance, we do not reject the null hypothesis and state
that the data do not show that the variation in drive times for the first worker is less
than the variation in drive times for the second worker.
3
October 28, 2025
, OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
Exercise 10. Two students are interested in whether or not there is variation in their test scores
for math class. There are 15 total math tests they have taken so far. The first
student’s grades have a standard deviation of 38.1. The second student’s grades
have a standard deviation of 22.5. The second student thinks his scores are lower.
State the null and alternative hypotheses.
Solution
Exercise 11. Two students are interested in whether or not there is variation in their test scores
for math class. There are 15 total math tests they have taken so far. The first
student’s grades have a standard deviation of 38.1. The second student’s grades
have a standard deviation of 22.5. The second student thinks his scores are lower.
What is the F Statistic?
Solution 2.8674
Exercise 13. Two students are interested in whether or not there is variation in their test scores
for math class. There are 15 total math tests they have taken so far. The first
student’s grades have a standard deviation of 38.1. The second student’s grades
have a standard deviation of 22.5. The second student thinks his scores are lower.
At the 5% significance level, do we reject the null hypothesis?
Solution Reject the null hypothesis. There is enough evidence to say that the variance of the
grades for the first student is higher than the variance in the grades for the second
student.
Exercise 14. Two cyclists are comparing the variances of their overall paces going uphill. Each
cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of
23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their
variances are the same or different.
State the null and alternative hypotheses
Solution
Exercise 15. Two cyclists are comparing the variances of their overall paces going uphill. Each
cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of
23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their
4
October 28, 2025
