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A clinical trial is run to compare weight loss programs. Participants are ran- domly assigned to one of the programs for 8 weeks. The outcome of interest is weight loss, defined as the difference in weight measured at the start of the study (baseline) and weight measured at the end of the study (8 weeks), measured in pounds. Three different weight loss programs are considered (a low calorie diet, a low fat diet and a low carbohydrate diet). For comparison purposes, a fourth group is considered as a control group. A total of twenty patients agree to participate in the study and are randomly assigned to one of the four diet groups. The researchers want to investigate whether there is a statistically significant difference in the mean weight loss among the four diets.
(i) State the null and alternative hypotheses.
(ii) What is an appropriate test statistic to use?
(iii) What is the decision rule? (Hint: what is the critical value and specify when you would reject the null hypothesis).
(iv) Suppose the treatment sum of squares is 75.8 and the error sum of squares 47.4, complete the hypothesis test and interpret the results of the test?
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