Question

You have collected two sets of samples with sample sizes of 16 and 20 respectively. What are the upper and lower critical values for the two-tailed F-Test for equality of two variances at 0.05 significance level?

Answer 1

The F hypothesis two tailed test is defined as:

Null hypothesis H0:  

Alternate hypothesis H1:

and F- test is given by :

,

where s₁²   and s₂² are the sample variances.

Let significance level be = 0.05 or 5 %

N₁ and N₂ be the sample sizes respectively.

The hypothesis that the two variances are equal is rejected if

OR

Now, we look at the F- table to at   and Degrees of freedom N₁-1 = 16-1 and N₂-1 = 20-1,

and this is our Upper tail critical value

Now, we use the fact that

( notice the degrees of freedom have interchanged in the denominator of Right Hand Side )

Therefore, we have to find the denominator by looking at the F-table,

We get ,  

Now,

and this is our lower tail critical value.

Therefore, our answer is:

1. Upper tail critical value = 2.61711774 ( given in pink color )

2. Lower tail critical value = 0.36061540 ( given in green color )