22. The following data are from a study of the number of pounds subjects lost after 3 months on a regimen of 1) only diet and exercise or 2) diet and exercise with a personal trainer or 3) diet and exercise with a support group. You want to determine if there is a statistically significant difference in the amount of weight lost depending on the regimen.

Diet and
Exercise Diet, Exercise,
Personal Trainer Diet, Exercise,
Support Group
4 11 7
6 14 9
12 9 10
5 22 6
8 15 12
7 8 16
10 12 11
17 17 8
4 24 19
12 30 14
9 8 13
5 16 7

a. What statistical test should you perform? ______________________

b. Compute F ____________

c. Is p > or < .05?

d. What is your conclusion regarding the results?

a. To determine if there is a statistically significant difference in the amount of weight lost depending on the regimen, you should perform a one-way analysis of variance (ANOVA) test.

b. To compute the F statistic, you first need to calculate the sum of squares (SS) for each factor (regimen) and the total sum of squares. Then, you can use these values to calculate the mean square (MS) for each factor and the error. The F statistic is the ratio of the mean square between groups (treatment) to the mean square within groups (error). To calculate F, you need to use the following formula:

F = MS_between / MS_within

c. To determine if the p-value is greater than or less than 0.05, you will need to perform the ANOVA test and obtain the p-value. If the p-value is less than 0.05 (p < 0.05), it indicates that there is a statistically significant difference between the regimens. If the p-value is greater than 0.05 (p > 0.05), it indicates that there is not enough evidence to conclude a statistically significant difference between the regimens.

d. Based on the obtained p-value, if it is less than 0.05 (p < 0.05), you can conclude that there is a statistically significant difference in the amount of weight lost depending on the regimen. If the p-value is greater than 0.05 (p > 0.05), you cannot conclude a statistically significant difference between the regimens.