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.

Type of Advice Human Advice Automated Advice No Advice At the beginning 93 64 68 99 65 56 118 106 64 89 117 102 After six months 119 198 106 167 242 97 141 115 151 121 166 74 After one year 104 186 144 212 250 128 173 140 101 193 185 125

a. Using a = 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 a = 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 a = 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 a = 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).

AppendixLO1