A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diets. Athletes are randomly assigned to three groups and placed on the diet for 6 weeks. The weight gains (in pounds) are shown here. At α = 0.05, can the researcher conclude that there is a difference in the diets?

A computer printout for this problem is shown. Use the P-value method and the information in this printout to test the claim.

Assume that all variables are normally distributed, that the samples are independent, and that the population variances are equal. Also, for each exercise, perform the following steps.
a. State the hypotheses and identify the claim.
b. Find the critical value.
c. Compute the test value.
d. Make the decision.
e. Summarize the results, and explain where the differences in the means are.
Use the traditional method of hypothesis testing unless otherwise specified.

Diet A Diet B Diet C 10 12 14 Computer Printout for Exercise 1Z ANALYSIS OF VARIANCE SOURCE TABLE df Sum of Squares Mean Square 50.548 6.530 Source p-value Bet Froups W/I Groups 7.740 101.095 71.833 0.00797 Total 13 172.929 DESCRIPTIVE STATISTICS Condit Means St Dev diet A diet B diet C 5.000 10.167 4.500 1.826 2.858 2.646