In a test of weight loss programs 120 subjects were divided

In a test of weight loss programs, 120 subjects were divided such that 30 subjects followed each of 4 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     310.430        3        103.47660   3.0357 0.032004   3.230795

Within Groups     3954.042       116        34.08657

Total                      4264.472     119

Solution

We are given the values of F critical and F sample

F critical = 3.230795

F sample = 3.0357

Now,

If F sample>F critical, we can reject the null hypothesis at the given significance level.

Therefore, the claim that the mean weight loss is the same for different diets is not true.