Question

The NIH wants to compare the mean weight loss for five different diets. They measure the weight loss (in pounds) of 5 men assigned to each of the diets for one month. The resulting data set is below.

Pounds	Diet
1.7	1
0.7	1
0.8	1
-0.6	1
-0.1	1
-1.2	2
-1.6	2
1.5	2
-1	2
0.6	2
0.8	3
-2.1	3
-1.2	3
2.4	3
0.1	3
-0.9	4
-3.3	4
-2.2	4
-2.2	4
-0.7	4
-0.7	5
-2.1	5
-1	5
-0.8	5
-3.2	5

b) What is the F statistic for the ANOVA? Give your answer to at least three decimal places.

c) Using a 0.01 level of significance, what is the critical point that one would compare to the F statistic in order to make a conclusion? Give your answer to three decimal places.

d) What is the P-value from the ANOVA? Give your answer to four decimal places.

e) What is the proper conclusion for NIH in this case?

-Fail to reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is larger than the critical point.

-Fail to reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is smaller than the critical point.   

-Reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is larger than the critical point.

-Diet 5 has the largest mean weight loss because the F statistic is larger than the critical point.

-Diet 4 has the largest mean weight loss because the F statistic is larger than the critical point.

Answer 1

hypothesis to be tested:

H0: all diets are equivalent in terms of mean weight loss

H1: atleast one diet differs in terms of mean weight loss

b) F-statistics value : 3.26835

c) Fcritical = 4.43 with df (4,20)

d) p-value = 0.032387

e) as p-val < 0.01, the result is not significant i.e. we reject the null hypothesis.

Hence we conclude that, we fail to reject the claim that all diets are equivalent in terms of mean weight loss because the F statistics is smaller than the critical value.