The recent Wall Street Journal article titled “The Power of a Gentle Nudge” cited a Stanford University study that researched the motivation of people to exercise. Participants were placed in one of three groups. After stating an exercise program, people in the first group received a phone call every three weeks from a trained health educator to ask about their exercise programs and encourage them to continue exercising. A second group received the same call from an automated system. The third group did not receive a call. The number of minutes spent exercising per week was recorded at the beginning of the program, after six months, and after one year. Suppose the following table provides data from this study. These data can also be found in the file exercise. xlsx.

a. Using α = 0.05, is there significant interaction ­between the type of advice and the length of the exercise program?

b. Using a two way ANOVA and α = 0.05, does the type of advice have an effect on the number of minutes the groups exercised per week?

c. Using a two way ANOVA and α = 0.05, does the length of the exercise program (the length of time since it began) have an effect on the number of minutes the groups exercised per week?

d. If warranted, determine which means are significantly different using α = 0.05.

e. Construct an interaction plot for the type of advice and length of the exercise program (the length of time since it began).

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Type of Advice No Advice 68 56 64 102 106 97 151 74 144 128 101 125 Humn Automated Advice Advice 64 65 106 At the beginning 93 118 89 119 After six months 141 121 104 212 173 193 198 242 115 166 186 250 140 185 After one year