Question

A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

Answer 1

Answer:

H0: $\sigma^2_1 = \sigma^2_2$

H1: $\sigma^2_1 \neq \sigma^2_2$

The statistic would be given by:

$F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25$

Step-by-step explanation:

Information given

$n_1 = 60$ represent the sample size 1

$n_2 =40$ represent the sample size 2

$s^2_1 = 8$ represent the sample variance 1

$s^2_2 = 10$ represent the sample variance 2

The statistic to check the hypothesis is given by:

$F=\frac{s^2_2}{s^2_1}$

Hypothesis to test

We want to test if the two variances are equal, so the system of hypothesis are:

H0: $\sigma^2_1 = \sigma^2_2$

H1: $\sigma^2_1 \neq \sigma^2_2$

The statistic would be given by:

$F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25$