A national business magazine reports that the mean age of retirement for women executives is 61.7. A women’s rights organization believes that this value does not accurately depict the current trend in retirement. To test this, the group polled a simple random sample of 82 recently retired women executives and found that they had a mean age of retirement of 60.8. Assuming the population standard deviation is 4.0 years, is there sufficient evidence to support the organization’s belief at the alpha = 0.02 level of significance? State the null and alternative hypotheses for the test.