409Practice08 - STAT 409 1 Practice Problems 8 Fall 2015 A Stepanov TaxesRUs Block is a national chain that prepares income tax returns for individuals

# 409Practice08 - STAT 409 1 Practice Problems 8 Fall 2015 A...

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STAT 409 Practice Problems 8 Fall 2015 A. Stepanov 1. Taxes’R’Us Block is 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 α = 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 α = 0.07 ? 2. In its advertising, Taxes’R’Us Block claims 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.)
3. Taxes’R’Us Block is currently under an IRS investigation for possible underreporting of income by its customers on federal income tax returns. 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 Block claims 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.