Reference: Applied Linear Statistical Models

Page: 728-729

16.32. Refer to Questionnaire color Problem 16.8. Suppose that the sample sizes have not yet been determined but it has been decided to sample the same number of supermarker parking lots for each questionnaire color. A reasonable planning value for the error standard deviation is = 3.0.

a. What would be the required sample sizes if: (1) differences in the response rates are to be detected with probability .90 or more when the range of the treatment means is 4.5, and (2) the a risk is to be controlled at .05?

b. If the sample sizes determined in part (a) were employed, what would be the minimum power of the test for treatment mean differences (using = .05) when the range of the treatment means is 6.0?

c. Suppose the chief objective is to identify the color with the highest mean response rate. The probability should be at least .99 that the best color is recognized correctly when the difference between the response rates for the best and second best colors is 1.5 percent points or more. What are the required sample sizes?

6.32. Refer to Questionnaire color Problem 16.8. Suppose that the sample sizes have not yet been determined but it has been decided to sample the same number of supermarket parking lots for each questionnaire color: A reasonable planning value for the error standard deviation is =3.0 Chapter 16 Single-Factor Studies 729 a. What would be the required sample sizes if: (1) differences in the response rates are to be detected with probability .90 or more when the range of the treatment means is 4.5, and (2) the risk is to be controlled at .05? b. If the sample sizes determined in part (a) were employed, what would be the minimum power of the test for treatment mean differences (using =.05 ) when the range of the treatment means is 6.0 ? c. Suppose the chief objective is to identify the color with the highest mean response rate. The probability should be at least .99 that the best color is recognized correctly when the difference between the response rates for the best and second best colors is 1.5 percent points or more. What are the required sample sizes