# Business Statistics

1)

Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

Sales ($)

129

133

147

159

138

143

Audit ($)

125

98

128

135

145

117

141

At the 0.005 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff?

picture Click here for the Excel Data File

1. State the decision rule. (Round your answer to 3 decimal places.)

Reject H0 if t > _________

2. Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)

Pooled variance ____________

3. Compute the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic ____________

2)

When only two treatments are involved, ANOVA and the Student’s t test (Chapter 11) result in the same conclusions. Also, formula120.mml. As an example, 14 randomly selected Introduction to History students were divided into two groups, one consisting of 6 students and the other of 8. One group took the course in the normal lecture format. The other group of 8 students took the course via the Internet. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups.

Traditional Lecture Internet

18 33

12 28

26 35

27 24

12 27

14 28

26

25

a-1. Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.)

Source SS df MS F

Factors ____ _____ _____ _____

Error _____ ______ ______ _______

Total _____ ______ _______ _________

a-2. Use a formula122.mml level of significance. (Round your answer to 2 decimal places.)

The test statistic is F _______

b.

Using the t test from Chapter 11, compute t. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

T = __________

3)

The null and alternate hypotheses are:

H0: μ1 ≤ μ2

H1: μ1 > μ2

A random sample of 28 items from the first population showed a mean of 108 and a standard deviation of 14. A sample of 21 items for the second population showed a mean of 98 and a standard deviation of 10. Assume the sample populations do not have equal standard deviations.

a.

Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)

Degrees of freedom _______

b. State the decision rule for 0.01 significance level. (Round your answer to 3 decimal places.)

Reject H0 if t> _______

c. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic ________

4)

The null and alternate hypotheses are:

H0 : μd ≤ 0

H1 : μd > 0

The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of four days last month.

Day

1 2 3 4

Day shift 10 12 15 18

Afternoon shift 8 9 13 16

At the .005 significance level, can we conclude there are more defects produced on the day shift?

1. State the decision rule. (Round your answer to 2 decimal places.)

Reject H0 if t > _______

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic _________

5)

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. A sample of 53 day-shift workers showed that the mean number of units produced was 355, with a population standard deviation of 24. A sample of 62 night-shift workers showed that the mean number of units produced was 363, with a population standard deviation of 32 units.

At the .01 significance level, is the number of units produced on the night shift larger?

1.

The decision rule is to reject H0: μd ≥ μn if z < ____________ . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

2.

The test statistic is z = _________ . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

6)

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months following the exercise program. Below are the results.

Employee Before After

1 7 4

2 6 4

3 7 3

4 5 2

5 4 2

6 5 6

7 6 3

8 5 7

At the 0.01 significance level, can he conclude that the number of absences has declined? Hint: For the calculations, assume the “Before” data as the first sample.

Reject H0 if t > _________. (Round your answer to 3 decimal places.)

The test statistic is ___________. (Round your answer to 3 decimal places.)

7) One of the music industry’s most pressing questions is: Can paid download stores contend nose-to-nose with free peer-to-peer download services? Data gathered over the last 12 months show Apple’s iTunes was used by an average of 1.57 million households with a sample standard deviation of .62 million family units. Over the same 12 months WinMX (a no-cost P2P download service) was used by an average of 2.18 million families with a sample standard deviation of .27 million. Assume the population standard deviations are not the same.

1.

Find the degrees of freedom for unequal variance test. (Round down your answer to nearest whole number.)

Degrees of freedom __________

2

State the decision rule for .10 significance level: H0: 1formula81.mmlA = 1formula81.mmlW; H1: 1formula81.mmlA ≠ 1formula81.mmlW . (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)

Reject H0 if t < ________ or t > ________

3.

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Value of the test statistic ___________

8)

A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan A is $50,600 with a standard deviation of $9,200. For a sample of 30 subscribers to Plan B, the mean income is $55,000 with a standard deviation of $7,100.

At the .025 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? Hint: For the calculations, assume the Plan A as the first sample.

The test statistic is__________________ . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)