# . You are planning to conduct a study to determine whether there is no difference in the average number of hours students study per week by year level (e.g. freshmen, sophomore, junior and senior.). What is the most appropriate test for conducting the test? (Hint: identify and classify the variables in this study)

Quiz 6 – ANOVA

1. You are planning to conduct a study to determine whether there is no difference in the average number of hours students study per week by year level (e.g. freshmen, sophomore, junior and senior.). What is the most appropriate test for conducting the test? (Hint: identify and classify the variables in this study)

a. One population mean test

b. Two population means test

c. One-way ANOVA

d. Two-way ANOVA with Replication

e. Chi-square Goodness of Fit Test

f. Chi-square Test for Independence

g. Regression and Correlation Analysis

2. You are planning to conduct a study to determine whether the average age of the residents of Ashland, OR is at least 55.6 years. What is the most appropriate test for conducting the test?

a. One population mean test

b. Two population means test

c. One-way ANOVA

d. Two-way ANOVA with Replication

e. Chi-square Goodness of Fit Test

f. Chi-square Test for Independence

g. Regression and Correlation Analysis

3. Professor of marketing Mark Siders gave you an assignment to see if a person’s gender can explain how much he/she spends (hours per day) surfing the Internet. What is the most appropriate test for conducting the test? (Hint: identify and classify the variables in this study)

a. One-way ANOVA

b. Two-way ANOVA with Replication

c. Chi-square Goodness of Fit Test

d. Chi-square Test for Independence

e. Regression and Correlation Analysis

An MBA director examined GMAT scores for the first 10 MBA applicants (assumed to be a random sample of early applicants) for four academic quarters.

Research question: do the mean GMAT scores of four early applicants differ by quarter?

Applicant

1

2

3

4

5

6

7

8

9

10

Fall

590

580

640

580

530

720

640

470

530

640

Winter

510

490

630

510

540

450

670

390

400

470

Spring

500

450

510

570

610

490

450

590

640

650

Summer

450

590

710

240

510

670

610

550

540

540

4. This problem involves which of the following tests?

a) Comparing proportions of two or more groups

b) One Factor ANOVA

c) Two Factor ANOVA without Replication

d) Two Factor ANOVA with Replication

e) None of the Above

5. What is the variable of interest in this problem?

a) Quarter

b) GMAT Score

c) Ten

d) Average

e) None of the above

6. What is the factor in this problem?

a) Quarter

b) GMAT Scores

c) Ten GMAT Scores

d) Average GMAT Score

e) None of the above

7. Which characteristic (parameter) of the variable of interest is being investigated in this problem?

a) Quarter

b) GMAT Score

c) Ten GMAT Scores

d) Average GMAT Score

e) None of the above

8. Give the critical F statistic for the test using a 0.025 significance level. _______

9. Give the computed F statistic for the test. ______________

10. At significance level 0.025, can the null hypothesis that all the GMAT score averages are the same for all quarters be rejected?

a) Yes

b) No

A market research firm is testing consumer reaction to a new shampoo among age groups in four regions. There are five consumers in each test panel. Each consumer completes a 10-question product satisfaction instrument with a 5-point scale (five is the highest rating) and the average score is recorded. Generate the appropriate outputs and perform the appropriate statistical tests to answer the questions below.

Northeast

Southeast

Midwest

West

Youth

3.9

4.0

3.7

4.1

4.3

3.9

4.2

4.4

4.1

4.0

3.6

3.9

3.9

3.7

3.3

3.9

4.4

4.0

4.1

3.9

College

4.0

4.0

3.7

3.8

3.8

3.8

3.7

3.7

3.6

3.7

3.6

4.1

3.8

3.9

4.0

3.8

3.8

3.6

3.6

4.1

Adult

3.2

3.8

3.7

3.4

3.4

3.5

3.3

3.4

3.5

3.4

3.5

3.8

3.8

4.0

3.7

3.8

3.6

3.4

3.7

3.1

Senior

3.4

2.9

3.6

3.7

3.5

3.6

3.4

3.6

3.6

3.4

3.3

3.3

3.1

3.1

3.1

3.4

3.2

3.5

3.3

3.4

11. What is the response variable in this problem?

a) Age group

b) Market regions

c) Satisfaction Rating

d) Average Rating

e) Shampoo

f) None of the above

12. What is/are the factor(s) in this problem?

a) Age Group and Rating

b) Age Group and Market Region

c) Market Region and Rating

d) Rating

e) Shampoo

f) None of the above

13. In testing whether the mean satisfaction ratings of the shampoo among the different market regions are the same, what is the critical F statistic (use a 0.05 significance level) that will be compared to the computed F statistic? ______

14. In testing whether there is a difference in the mean satisfaction rating of the shampoo among the different age groups, what is the computed F statistic (that will be compared to the critical F statistic)? ______

15. In testing whether there is an interaction effect on the satisfaction rating of the shampoo in at least one combination of age group and market region levels, what is the p-value that will be compared to the significance level? ______

16. At significance level 0.05, is there a difference in the mean satisfaction rating of the shampoo by the consumers by age group?

a) Yes b) No

17. Which of the 4 age groups shows the lowest average satisfaction rating for the shampoo?

a) Youth

b) College

c) Adult

d) Senior

e) None – all show the same average satisfaction level per ANOVA test

18. Which of the 4 age groups gives the highest average satisfaction rating for the shampoo?

a) Youth

b) College

c) Adult

d) Senior

e) None – all show the same average satisfaction level per ANOVA test

19. At significance level 0.05, is there a difference in the satisfaction rating of the shampoo by the consumers of the different regions?

a) Yes b) No

20. Which of the 4 regions shows the lowest average satisfaction rating for the shampoo?

a) Northeast

b) Southeast

c) Midwest

d) West

e) None – all show the same average satisfaction level per ANOVA test

21. Which of the 4 regions shows the highest average satisfaction rating for the shampoo?

a) Northeast

b) Southeast

c) Midwest

d) West

e) None – all show the same average satisfaction level per ANOVA test

22. At significance level 0.05, is there an interaction effect on satisfaction on the shampoo’s rating in at least one combination of factor levels of age of customers and region where they are from?

a) Yes b) No

23. For the southeast region, which age group gives the highest average satisfaction rating for the shampoo?

a) Youth

b) College

c) Adult

d) Senior

24. Among the youth consumers, in which region did the product receive the lowest average satisfaction rating?

a) Northeast

b) Southeast

c) Midwest

d) West

25. Among the Senior consumers, in which region did the product receive the highest average satisfaction rating?

a) Northeast

b) Southeast

c) Midwest

d) West