Suppose there are two samples drawn from two normally distributed populations as shown in the following table:

Sample Size

Sample Variance

Sample One

121

66

Sample Two

61

60



Now use the formula in the previous section to determine if the two populations have the same variance, and if the confidence level is equal to 0.95. $\mathrm{\beta}$ is equal to one in this case.
1.

Determine the null hypothesis:


Null Hypothesis: The two studied populations have the same variance.

2.

Substitute the information into the formula:


$f=\frac{66}{1\cdot 60}=1.1$


${d}.f=\left(1211,611\right)=\left(120,60\right)$


$p\mathrm{value}=2*\mathrm{Probability}\left(F>1.1\right)=0.69078$ (twotailed)


$F\u02dc\mathrm{FRatio}\left(120,60\right)$


This statistical test does not provide enough evidence to conclude that the null hypothesis is false, so we fail to reject the null hypothesis.
