Use the summary stats below to test the claim that the samples come from from the populations with different variances. Use a significance level of 0.05.
Sample A Sample B
n=28 n=41
x1=19.2 x2=23.7
s=5.2 s=5.28

Question

Use the summary stats below to test the claim that the samples come from from the populations with different variances. Use a significance level of 0.05.
Sample A Sample B
n=28 n=41
x1=19.2 x2=23.7
s=5.2 s=5.28

kropot72 · Answer

The F test can be applied in this case. It is a test that two independent samples have been drawn from populations with the same variance; the null hypothesis being that the samples are drawn from populations with the same variance.
For sample B
$$s ^{2}=27.8784$$
For sample A
$$s ^{2}=27.04$$
We now rename sample B to sample 1, the reason being it has the greater variance. Sample B is renamed sample 2.
$$n _{1}=41\ \ \ \ n _{2}=28$$
The test statistic F is given by
$$F=\frac{s _{1}^{2}}{s _{2}^{2}}=\frac{27.8784}{27.04}=1.031$$
The degrees of freedom are
$$v _{1}=41-1=40\ \ \ \ \ v _{2}=28-1=27$$
We now need to find the critical value for 
$$F _{40,\  27}$$
The F test is a two-tail test, so the percentage point to be looked up is
$$\frac{1}{2}\times5\%=2.5\%$$
From the F distribution table for 2.5% points, The critical value for F 40, 27 is approximately 2.
Since 1.031 < 2 the null hypothesis is accepted and the claim that the samples come from from populations with different variances is rejected.

ankit042 · Answer

@kropot72 can you please some resource for learning more about F test..thanks!

kropot72 · Answer

@ankit042 The information at this link could be of some help to your understanding of this application of the F test: http://en.wikipedia.org/wiki/F-test_of_equality_of_variances