Dataset Information: You are a researcher examining the effect of different weight loss programs on change in weight after four months. You obtain a sample of 150 total patients, all similar ages, who are seeking to lose weight for health reasons with the approval and oversight of their primary care physician. These patients choose to participate in one of three programs, for a total of 50 patients in each program: 1. Diet alone 2. Exercise alone 3. Diet and exercise in combination After participating in their chosen program for four months, patients’ change in weight is measured in pounds. You would like to compare mean weight change between the three groups to determine the effect of type of weight loss program. Your dataset contains a unique identifier for each patient (“patient_ID”) along with a group assignment for each patient (“program”). The value for “program” is either “diet,” “exercise,” or “diet and exercise” depending on which program the patient participated in. Finally, there is a variable called “weight_change” which shows patients’ weight change after program participation, measured in pounds. This dataset is an Excel file entitled “Weight Dataset.xlsx” which can be found on Blackboard under Course Content > Module 11: ANOVA > Module 11 Assignment. You decide to compare mean weight change values across the three programs using one-way ANOVA with a significance level of α=0.05. This will help you to determine the effect of program on weight change. Your hypotheses are as follows: H0: 𝜇𝐷𝑖𝑒𝑡 𝑎𝑙𝑜𝑛𝑒 = 𝜇𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝑎𝑙𝑜𝑛𝑒 = 𝜇𝐷𝑖𝑒𝑡 𝑎𝑛𝑑 𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒 H1: At least one 𝑋̅ is different
Assignment Instructions: Using complete sentences, answer the following questions from your analysis:
What is the mean weight change for each of the three weight loss program groups (in pounds)?
What is the F test statistic value from the ANOVA that you performed in SPSS?
You have set your significance level at α=0.05 and performed a one-way simple ANOVA. Using this information and the two sets of degrees of freedom from your SPSS output, what is the critical F value for your test? (Hint: use Table B.3 in Appendix B in your textbook. If you don’t see the exact number of degrees of freedom in your textbook, select the critical F value that corresponds to the closest number of degrees of freedom.)
Does your F test statistic value exceed the critical F value? What can you conclude about the three weight loss programs as a result?
discuss the null hypothesis in your answer, and whether you reject or fail to reject it
