Problem 1: A random sample of 81 students at a local university showed that they work an average of 100 hours per month. The population standard deviation is known to be 27 hours. Answer the 4 questions below

1) What is the point estimate for the mean hours per month all students at the university work?

2) 95% confidence interval is ( , )

3) 99% confidence interval is ( , )

4) Which interval is wider and why?

Problem 2: The manager of an auto repair wants to advertise one price for an engine tune-up, with parts included. Before he decides the price to advertise, he needs a good estimate of the average cost of tune-up parts. A sample of 20 customer invoices for tune-ups has been selected and the costs of parts, rounded to the nearest dollar, are listed below. Answer the three questions below.

150 78 93 57 75 52 99 80 105 62

104 74 62 68 97 73 77 65 80 109

1) What is the point estimate for the average cost of all tune-up parts?

2) 99% confidence interval is ( , )

3) If the manager thinks the 99% confidence is too wide and wants to narrow it down, what can he do?