Hypothesis test for the population variance or standard deviation

Can you answer this now? 

The human resources department of a major corporation announced that the number of people interviewed by the corporation in one month has a mean of  and a variance, , of . The management of the corporation suspects that the variance exceeds . A random sample of  months yielded a mean of  interviews, with a variance of . If we assume that the number of people interviewed by the corporation in one month follows an approximately normal distribution, is there enough evidence to conclude, at the  level of significance, that the management’s claim is correct?

Perform a one-tailed test.

Questions:

The null hypothesis

The alternate hypothesis 

Test Statistic

Critical Value

Can you support the claim that the variance of the number of people interviewed by the corporation in one month exceeds 271?