Can a Brief Diet Intervention Help Depression? 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. Depression levels were measured at the beginning of the experiment and then again three weeks later. The response variable is the reduction in depression level (as measured by the DASS survey) at the end of the three weeks. Larger numbers mean more improvement in depression symptoms. Test whether these experimental results allow us to conclude that, on average, improvement of depression symptoms 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.

Give value of the sample statistic accurate to one decimal place.

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

State the conclusion in context.

Reject H₀. Mean depression levels are reduced from three weeks of healthy eating.

Reject H₀. We don't have enough evidence to conclude that healthy eating changes depression levels.

Do not reject H₀. Mean depression levels are reduced from three weeks of healthy eating.

Do not reject H₀. We don't have enough evidence to conclude that healthy eating changes depression levels