Please review the question below.

Problem 3. [25 pts] The Internal Revenue Service (IRS) wants to determine if a waiter working at an expensive restaurant has tip income more than what he reported. Let / be the mean tip the waiter got on all the receipts (more than 10,000 receipts). The waiter's tax return declared that the average tip was / = $10.00 per bill. The IRS took a simple random sample of n = 100 from all his receipts. and this sample yields an average tip of a = $12.00 and a sample standard deviation of s = $8.0. Let the significance level o = 0.05. (a) [10 pts] Do these data support a decision that the waiter underreported his tip income? Con- duct an appropriate hypothesis test in two ways using the statistical tables provided: (1) finding the critical region; (2) finding the range of the p-value. (b) 3 pts] Based on the conclusion obtained in (a), can we directly say the value 10 falls outside the 95% confidence interval of a without computing the confidence interval? Why? (c) [12 pts] If it is known that the true standard deviation o = $9.0, conduct an appropriate hypothesis test to get your conclusion by the method of computing the p-value. In this case, if = $11.00, what is the power of the test