Can a Brief Diet Intervention Change BMI? Exercise 2.209 introduces a study investigating whether a brief diet intervention might improve depression symptoms. In the study, 75 college-age students with elevated depression symptoms and relatively poor diet habits were randomly assigned to either a healthy diet group or a control group. While the study was explicitly studying the impact of a healthy diet on depression levels, the researchers also measured Body Mass Index (BMI) of all the participants at the beginning of the experiment and then again three weeks later. The response variable is the reduction in BMI, so larger numbers indicate greater reduction. Test whether these experimental results allow us to conclude that, on average, change in BMI is higher for those who eat a healthy diet for three weeks than for those who don't. The data is available on StatKey and in DietDepression. Let Group 1 represent those with a healthy diet and Group 2 represent those with no diet change.

a) State the null and alternative hypotheses.

b) Give notation of the sample statistic.

c) Give value of the sample statistic accurate to three decimal places.

d) Use a randomization distribution to find the p-value. Give your answer accurate to three decimal places.

e) State the conclusion in context.

• Reject H₀. Mean BMI is reduced from three weeks of healthy eating.
• Reject H₀. We don't have enough evidence to conclude that healthy eating for three weeks changes mean BMI.
• Do not reject H₀. Mean BMI is from three weeks of healthy eating.
• Do not reject H₀. We don't have enough evidence to conclude that healthy eating for three weeks changes mean BMI.