Question

The effectiveness of three diet plans was analyzed. Use a significant level 0.05 to test the claim that the mean weight loss among all diet plans is the same given the following ANOVA results.
F= 0.352
P-value= 0.878
F critical= 2.69
A) There is enough evidence to reject the null hypothesis.
B) There is not enough evidence to reject the null hypothesis
C) It cannot be determined
D) There is sufficient evidence to fail to reject the null hypothesis

Answer 1

Null and alternative hypothesis of ANOVA test:

$$H _ {0}: \mu_ {1} = \mu_ {2} = \mu_ {3}$$

$H_{1}$: at least one of means is different

P-value of the ANOVA test equals to

$$p = 0.878$$

The significance level is given to be $\alpha = 0.05$.

Since $p > \alpha$ we fail to reject the null hypothesis. There is no enough evidence to reject the null hypothesis at significance level $\alpha = 0.05$.

ANSWER: B