You are interested in testing if there is a difference in weight-loss between 3 popular diet types; low calorie, low fat and low carb. Participants are randomly assigned one of the three groups or a...

You are interested in testing if there is a difference in weight-loss between 3 popular diet types; low calorie, low fat and low carb. Participants are randomly assigned one of the three groups or a control group. The control group will be told that are participating in a weight-loss study, but will not be following any particular diet. This is to study the placebo effect, weight-loss from just participating in the study.
At the start of the study,each participant's weight is recorded in pounds. After 8 weeks they are weighed again, and the weight difference is recorded. A positive value represents a weight loss while a negative value represents a weight gain. Test at 5% significance.

Test Statistic:
P-Value: