USA Today reports (Gary Stoller, “Hotel Bill Mistakes Mean Many Pay Too Much”) that George Hansen, CEO of Wichita-based Corporate Lodging Consultants, conducted a recent review of hotel bills over a 12-month period. The review indicated that, on average, errors in hotel bills resulted in overpayment of $11.35 per night. To determine if such mistakes are being made at a major hotel chain, the CEO might direct a survey yielding the following data:

9.99 9.87 11.53 12.40 12.36 11.68 12.52 9.34 13.13 10.78 9.76 10.88 10.61 10.29 10.23 9.29 8.82 8.70 8.22 11.01 12.40 9.55 11.30 10.21 8.19 10.56 8.49 7.99 8.03 10.53 The file OverPay contains these data.

a. Conduct a hypothesis test with a  0.05 to determine if the average overpayment is smaller than that indicated by Corporate Lodging Consultants.

b. If the actual average overpayment at the hotel chain was $11 with an actual standard deviation of $1.50, determine the probability that the hypothesis test would correctly indicate that the actual average is less than $11.35.