STAT 400 Practice Problems 4 Summer 2018 A. Stepanov 1.Taxes’R’Us Blockis a national chain that prepares income tax returns for individuals. The president of the company wants an average number of 5 customers per clerk per day. On April 15, a random sample of 64 clerks shows the average number of customers per clerk at 4.75. Assume that the overall standard deviation of 1.15. a) Test whether the average number of customers per clerk on April 15 was 5 or it was different. Use = 0.05. b) Suppose the actual overall average number of customers per clerk on April 15 was 4.8. Was the decision you made in part (a) correct? If not, what type of error has been made?c) What is the p-value of the test in part (a)d) Using the p-value obtained in part (c), would you accept or reject the null hypothesis from part (a) at = 0.072.In its advertising, Taxes’R’Us Blockclaims that the overall average bill for its services does not exceed $75. A consumer agency obtains a random sample of 20 tax returns prepared by the company and finds the average preparation bill for those 20 to be $79.82 with a sample standard deviation of $10.30. (Assume the amounts of the service fees are normally distributed.) a) We would like to test the claim made in the ad. Perform the appropriate test at a 10% significance level. b) What is the p-value of the test in part (a)c) Was the decision you made in part (a) correct? If not, what type of error has been made? d) Construct a 95% confidence interval for the average bill for services at this firm. ? ? ?

3.Taxes’R’Us Blockis currently under an IRS investigation for possible underreporting of income by its customers on federal income tax returns. a) A random sample of 225 Taxes’R’Us Block’s customers is obtained, of which 72 underreported their income. Construct a 90% confidence interval for the proportion of all Taxes’R’Us Block’s customers who underreport their income. b) IRS claims that at least 35% of all Taxes’R’Us Block’s customers underreported their income. Perform the appropriate test using a 5% level of significance. c) What is the p-value of the test in part (b)d) Find the minimum sample size required for estimating the proportion of all Taxes’R’Us Block’s customers who underreport their income to within 3% with 90% confidence, if it is known that this proportion is between 0.25 and 0.35. 4.In its advertising, Taxes’R’Us Blockclaims that the average tax return for a family with two children is at least $700. A random sample of 81 tax returns shows a sample mean of $674 and a sample standard deviation of $117. a) Perform the appropriate test at a 1% level of significance. b) What is the p-value of the test in part (a)c) Using the p-value obtained in part (b), would you accept or reject the null hypothesis from part (a) at = 0.045.? ? ?