Question

The human resources department of a large investment bank announced that the number of people it interviews monthly has a mean of 110, with a variance of 268.96. The management of the bank suspects that the variance exceeds 268.96. Suppose that the management wants to take a small sample of months and carry out a hypothesis test to see if its suspicions have support. State the null hypothesis and the alternative hypothesis that it would use for this test.

Answer 1

Answer:
`H_0: \sigma^2= 268.96\\\\ H_a:\sigma^2> 268.96`

Explanation:

Given : The human resources department of a large investment bank announced that the number of people it interviews monthly has a mean of 110, with a variance of 268.96.

The management of the bank suspects that the variance exceeds 268.96.

Since the claim is about variance, so the hypothesis will also be about variance.

Let
`\sigma^2` denotes the population variance.

Then, the null and alternative hypothesis will be :_

`H_0: \sigma^2= 268.96\\\\ H_a:\sigma^2> 268.96`