Answer to Question #111028 in Statistics and Probability for Gnanamani

Question

Three samples each of size 5 were drawn from 3 uncorrelated normal populations with equal variances. Analyse the hypothesis that the population means are equal at 5%level.
Sample-1
10
12
9
16
13

Sample-2
9
7
12
11
11

Sample-3
14
11
15
14
16

Answer 1

Here we can see that the F-value is greater than the F-critical value for the alpha level selected (0.05). Therefore, we have evidence to reject the null hypothesis and say that at least one of the three samples have significantly different means and thus belong to an entirely different population.