Question

Calculate the test statistic F to test the claim that  = . Two samples are randomly selected from populations that are normal. The sample statistics are given below.

n₁ = 25 n₂ = 30

= 7.942  = 4.95

Answer 1

From the question, it is not clear as to what is the alternative hypothesis. I assume it is two sided alternative.

We are given that

Null and alternative hypothesis:

Level of significance:

Test statistic: will follow an F-distribution with df.

The critical region for a two tailed alternative is

Since, the calculated value of F falls in the region of rejection, we reject the null hypothesis. Hence, we conclude that  there is enough evidence to claim that the population variance is different than the population variance ​, at the .

-----------------------------------------------------------------------------Please replace the following parts in case the alternative is different ------------------------------------------------------------------------------------

In case then the critical region is

Since, the test statistic doesn't fall in the rejection region, the null hypothesis is not rejected and hence we conclude that hat  there is not enough evidence to claim that the population variance is less than the population variance ​, at the .

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In case then the critical region is

Since, the calculated value of F falls in the region of rejection, we reject the null hypothesis. Hence, we conclude that  there is enough evidence to claim that the population variance is greater than the population variance ​, at the