Answer to Question #277755 in Statistics and Probability for navvvv

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. [F at (24,21) at 5% level of significance is 2.05]

Answer 1

Solution

We are given:

$Sample\:size\:\left(n_1\right)=25$

$Sample\:size\:\left(n_2\right)=22$

$S_1^2=16$

$S_2^2=8$

Now we have to compute:

$H_o:\sigma_1^2=\sigma_2^2$

$H_o:\sigma_1^2 \ne$ $\sigma_2^2$

The test statistic is as follows:

$F=\frac{16}{8}$ $=2$

$F_{\frac{0.5}{2},\:24,\:21}=2.05$

Here $F<F_{\frac{0.5}{2},\:24,\:21}$

Thus, $H_o$ is accepted.We can say that their is no variability in mathematical skills in one school of other school.