# Question

A medical researcher designed an experiment to study the impact of three exercise regimens (30, 60, and 90 minutes per week) on the total blood cholesterol level in active adult males.

The researcher was concerned that the effect of the type of exercise program on cholesterol might also depend on the age of the individual. Nine participants in each of three age groups (A1: 20– 29, A2: 30– 39, A3: 40– 49) were obtained from five fitness centers. The total blood cholesterol level of the participants were measured both prior to the start of the study and after 6 months on the exercise regimens. The reductions in total blood cholesterol level are given in the following table.

a. Identify the design by name.

b. Write a model for this study, identifying all the terms in the model.

c. Do the data support the research hypothesis that the mean reduction in cholesterol increases with an increase in exercise? Use α = .05 in reaching your conclusion.

d. Is your answer in part (c) consistent across all three age groups? Support your answer with a p- value from an appropriate test of hypotheses.

e. Assume that the effectiveness of the three exercise regimens differed for the three age groups. Group the three exercise regimens separately for each age group using an overall Type I error rate of .05.

The researcher was concerned that the effect of the type of exercise program on cholesterol might also depend on the age of the individual. Nine participants in each of three age groups (A1: 20– 29, A2: 30– 39, A3: 40– 49) were obtained from five fitness centers. The total blood cholesterol level of the participants were measured both prior to the start of the study and after 6 months on the exercise regimens. The reductions in total blood cholesterol level are given in the following table.

a. Identify the design by name.

b. Write a model for this study, identifying all the terms in the model.

c. Do the data support the research hypothesis that the mean reduction in cholesterol increases with an increase in exercise? Use α = .05 in reaching your conclusion.

d. Is your answer in part (c) consistent across all three age groups? Support your answer with a p- value from an appropriate test of hypotheses.

e. Assume that the effectiveness of the three exercise regimens differed for the three age groups. Group the three exercise regimens separately for each age group using an overall Type I error rate of .05.

## Answer to relevant Questions

Refer to Exercise 15.37. a. If this experiment was conducted again, would you recommend including the factor associated with center in your model and analysis? b. What was the relative efficiency of the center factor in the ...Refer to Exercise 15.41. Based on a residuals analysis, do the necessary conditions for conducting the test of hypotheses appear to be valid? A researcher designs a study to evaluate three dietary supplements that are reputed to lower the systolic blood pressure reading for people who have high blood pressure. A inert supplement is included to evaluate the placebo ...Refer to Exercises 16.15 and 16.16. a. Assuming parallelism of the response lines, perform a test for block differences adjusted for the covariate. Use α = .05. b. How might you partition the block sum of squares into five ...Refer to Exercise 16.23. Researchers have opined that in many forests the Shannon index is a more complete measure of biodiversity than Fisher’s alpha. Repeat Exercises 16.23 and 16.24 using Shannon’s index in place of ...Post your question

0