Chapter 12 Review Exercises

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section 12.1

Question 12.141

1. For the following data, assume that the ANOVA assumptions are met, and calculate the measures in (a)–(b).

Sample A Sample B Sample C Sample D
  1. and
  3. SSTR
  4. SSE
  5. SST
  6. MSTR
  7. MSE

12.99.1

(a) , (b) 10 (c) 10,000 (d) 1,157.5 (e) 11,157.5 (f) 3,333.3333 (g) 3.910472973 (h) 852.4117985

Question 12.142

2. Construct the ANOVA table for the statistics in Exercise 1.

For Exercises 3–5, assume that the ANOVA assumptions are met and perform the appropriate analysis of variance using .

Question 12.143

medicaltreatmt

3. Differences in Medical Treatments. A psychologist is interested in investigating whether differences in mean client improvement exist for three medical treatments. Seven clients undergoing each medical treatment were asked to rate their level of satisfaction on a scale of 0 to 100. The data are provided in the following table.

Medical
treatment 1		 Medical
treatment 2		 Medical
treatment 3
75 75 100
100 100 100
0 25 50
50 75 90
50 50 75
40 75 75
25 60 90

12.99.3

: Not all the population means are equal. population mean level of satisfaction for Medical Treatment 1. population mean level of satisfaction for Medical Treatment 2. population mean level of satisfaction for Medical Treatment 3. . Reject if . . Since is not we do not reject . There is insufficient evidence that not all of the population means are equal.

image

Question 12.144

customersatisfy

4. Customer Satisfaction. The district sales manager of a local chain store wants to determine whether significant differences exist in the mean customer satisfaction among the four franchise stores in her district. Customer satisfaction data were gathered over seven days at each of the four stores. The resulting data are summarized in Table 13.

Table 12.58: TABLE 13 Customer satisfaction in four stores
Store A Store B Store C Store D
50 60 25 75
40 45 30 60
60 70 50 80
60 70 30 90
50 60 40 70
45 65 25 85
55 70 45 95

section 12.2

For Exercises 5–7, use the summary statistics to calculate the value of the test statistic for the Bonferroni method.

Question 12.145

5. , , MSE = 1250, ,

12.99.5

Question 12.146

6. , , MSE = 1250, ,

Question 12.147

7. , , MSE = 1250, ,

12.99.7

Question 12.148

8. Perform multiple comparisons using the Bonferroni method at level of significance for the data in Exercises 5–7. Assume the requirements are met. Do the following:

  1. For each hypothesis test, state the hypotheses and the rejection rule.
  2. Use the value of from Exercises 5–7 for each hypothesis test.
  3. Find the Bonferroni-adjusted -value for each hypothesis test.
  4. For each hypothesis test, state the conclusion and the interpretation.

For Exercises 9–11, use the summary statistics to calculate the value of the test statistic for Tukey's test.

Question 12.149

9. , , MSE = 14,400, ,

12.99.9

Question 12.150

10. , , MSE = 14,400, ,

Question 12.151

11. , , MSE = 14,400, ,

12.99.11

Question 12.152

12. Find the Tukey critical value for experimentwise error rate , , , .

Question 12.153

13. Perform multiple comparisons using Tukey's test at experimentwise error rate , for the data in Exercises 9–11. Assume the requirements are met. Do the following.

  1. For each hypothesis test, state the hypotheses.
  2. Use the value of from Exercise 12, and state the rejection rule.
  3. Use from Exercises 9–11 for each hypothesis test.
  4. For each hypothesis test, state the conclusion and the interpretation.

12.99.13

(a) Test 1: ; Test 2: . Test 3: . (b) . Reject if . (c) Test 1: ; Test 2: ; Test 3: (d) Test 1:, which is not ; therefore we do not reject . There is insufficient evidence at the level of significance that the population mean of Population 1 differs from the population mean of Population 2. Test , which is ; therefore we reject . There is evidence at the level of significance that the population mean of Population 1 differs from the population mean of Population 3. Test , which is not ; therefore we do not reject . There is insufficient evidence at the level of significance that the population mean of Population 2 differs from the population mean of Population 3.

712

section 12.3

Question 12.154

14. For the partially completed randomized block ANOVA table, do the following:

  1. Provide the hypotheses.
  2. Complete the missing entries in the table.
  3. Use technology to find the -value. For level of significance , provide the conclusion and the interpretation.
Source Sum of
squares		 Degrees of
freedom		 Mean
square
Treatments — — — 2
Blocks 420 5 —
Error 200 20 10
Total 700 —

Question 12.155

genderindustry

15. The following table represents an excerpt from a U.S. Census Bureau report on the numbers of small businesses owned by females and males in four industries. Perform the randomized block design ANOVA using level of significance .

Block: Industry Factor of interest:
Gender of owner
Female Male
Retail 9 11
Real estate 5 11
Health care 20 10
Entertainment 3 5

12.99.15

: Not all of the population means are equal. Reject if . The , which is not ; therefore we do not reject . There is insufficient evidence at level of significance that the population mean number of small businesses owned by women differs from the population mean number of small businesses owned by men.

section 12.4

For the data in Exercises 16 and 17, draw an interaction plot and determine whether there exists no interaction, some interaction, or substantial interaction.

Question 12.156

16.

Factor B Factor A
100 95 120 115 85 80
120 125 150 155 100 95

Question 12.157

17.

Factor B Factor A
10 8 3 2 12 9
3 4 11 7 5 2

12.99.17

There is significant interaction between Factor A and Factor B.

image

For Exercises 18 and 19, use level of significance to do the following for the indicated data:

  1. Test for interaction. Confirm that the result agrees with the interaction plot you constructed.
  2. If appropriate, test for the Factor A effect.
  3. If appropriate, test for the Factor B effect.

Question 12.158

18. Data in Exercise 16

Question 12.159

19. Data in Exercise 17

12.99.19

(a) : There is no interaction between carrier (Factor A) and type (Factor B). : There is interaction between carrier (Factor A) and type (Factor B). Reject if the . The , which is ; therefore we reject . There is evidence of interaction between carrier (Factor A) and type (Factor B) at level of significance . This result agrees with the interaction plot in Exercise 17. (b) Not appropriate (c) Not appropriate