PART A Clients can choose between three diets at a weight-loss treatment center.

Question

PART A

Clients can choose between three diets at a weight-loss treatment center. An experiment was performed to determine if there is a difference between the diets. Fifteen patients were randomly selected and divided evenly into three groups of five for each diet. After 30 days the weight change (in pounds) for each client was recorded as shown below.

Diet A: 4, 4, 5, 5, 7

Diet B: 5, 6, 6, 7, 7

Diet C: 7 ,8, 8, 9, 9

What is the alternative hypothesis?

a) At least one of the diet means is not equal.

b) None of the diet variances are equal.

c) All of the diet means are equal.

d) All of the diet variances are equal.

e) None of the diet means are equal.

PART B

What is the critical value at the 0.05 level of significance?

a) 3.89

b) 6.93

c) 3.29

d) 19.4

Explanation / Answer

Part A

Nul Hypothesis:

H0: All diet means are equal

Alternative Hypothesis:

H1: At least one of the diet means is not equal.

Part B

F-test statistic: 13.52

the critical value at the 0.05 level of significance

F-critical value with 2 and 12 degrees of freedom = 3.89

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