An employment information service claims the mean annual salary for senior level product engineers is $96,000. The annual salaries (in dollars) for a random sample of 16 seniors level product engineers are showh below. At a = 0.05, test the claim that the mean salary is $96,000. Complete part (a) through (e) below. Assume the population is normal distrubited

100,675 96,227 93,629 112,612 82,457 74,154 74,154 76,939 80,953

102,444 76,219 104,77 103,958 91,174 82,093 85,126 85,126 110,328

a) Identify the claim and state the null hypothesis and alternative hypothesis

b) Find the critical value(s) and iidentify the rejection region(s)

c) Compute the standardized test statistc.

d) Decide wether to reject or fail to reject the null hypothesis at the 5% level of significance. Justify your answer.

e) Interpret the devision in the context of the original claim.

(Round off answers to the nearest thousandth, as needed)