Question

In a test of weight loss​ programs, 160 subjects were divided such that 32 subjects followed each of 5 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.025 significance level to test the claim that the mean weight loss is the same for the different diets.

Source of Variation	SS	df	MS	F	​P-value	F crit
Between Groups	554.416	4	138.60402	4.4411	0.001999	2.869395
Within Groups	4837.455]	155	31.20939
Total	5391.871	159

Should the null hypothesis that all the diets have the same mean weight loss be​ rejected?

A.

YesYes​,

because the​ P-value is

greater thangreater than

the significance level.

B.

YesYes​,

because the​ P-value is

less thanless than

the significance level.

C.

NoNo​,

because the​ P-value is

less thanless than

the significance level.

D.

NoNo​,

because the​ P-value is

greater thangreater than

the significance level.

Answer 1

The correct option is (B), i.e., Yes, because the P-value is less than the significance level.

The null and alternative hypothesis, for this test are:

mean weight loss is the same for the different diets.

At least mean weight loss is different for one of the diet.

The test-statistic is given as-

And if the test-statistic, i.e., is greater than the critical value, i.e., , then we Reject the null hypothesis.

Since,

So, we conclude that the sample data provides sufficient evidence to reject null hypothesis, H₀ .

We can also conclude the same by using a P-value method.

In P-value method, if

Given:

Since,

So, at significance level of sample data provides sufficient evidence to reject null hypothesis H₀ , hence we conclude that, we did not find evidence to believe that All the diets have the same mean weight loss.