4.A national business magazine reports that the mean age of retirement for women executives is 61.0. A women's rights organization believes that this value does not accurately depict the current trend in retirement. (30pts)

a.To test this, the group polled a simple random sample of 25 recently retired women executives and found that they had a mean age of retirement of 61.5 and a sample standard deviation of 2.5 years, is their sufficient evidence to support the organization's belief at the = 0.05 significant level. Assume distribution is normally distributed.

b.Based on your decision, which type of error could the sample data have led you to make? Explain what that means in the context of the question.