Question

The students of same age group from two different schools were compared for variability in their mathematical skill. A random sample of 25 pupils from one school had a variance of 16 marks while a random sample of 22 pupils from the other school had a variance of 8 marks. Examine if

the difference in variability is significant IF at (24.21) at 5% level of significance

Answer 1

F test for variances, using F distribution (df_num=24,df_denom=21) (two-tailed) 

$H_0:\sigma_1=\sigma_2$ , there is no difference in variability in two groups

$H_a:\sigma_1\neq\sigma_2$ , there is difference in variability in two groups

$F=\frac{\sigma_1^2}{\sigma_2^2}=\frac{16}{8}=2$

critical value:

$F_{crit}=2.05$

Since $F<F_{crit}$ we accept null hypothesis. There is no difference in variability in two groups.