91Ó°ÊÓ

Hypotheses For each of the following, write out the null and alternative hypotheses, being sure to state whether the alternative is one-sided or two- sided. a) A company knows that last year \(40 \%\) of its reports in accounting were on time. Using a random sample this year, it wants to see if that proportion has changed. b) Last year, \(42 \%\) of the employees enrolled in at least one wellness class at the company's site. Using a survey, it wants to see whether a greater percentage is planning to take a wellness class this year. c) A political candidate wants to know from recent polls if she's going to garner a majority of votes in next week's election.

Testing cars A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop's license if they find significant evidence that the shop is certifying vehicles that do not meet standards. a) In this context, what is a Type I error? b) In this context, what is a Type II error? c) Which type of error would the shop's owner consider more serious? d) Which type of error might environmentalists consider more serious?

Quality control Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they will halt the assembly process until the problem can be identified and repaired. a) In this context, what is a Type I error? b) In this context, what is a Type II error? c) Which type of error would the factory owner consider more serious? d) Which type of error might customers consider more serious?

Faulty or not? You are in charge of shipping computers to customers. You learn that a faulty disk drive was put into some of the machines. There's a simple test you can perform, but it's not perfect. All but \(4 \%\) of the time, a good disk drive passes the test, but unfortunately, \(35 \%\) of the bad disk drives pass the test, too. You have to decide on the basis of one test whether the disk drive is good or bad. Make this a hypothesis test. a) What are the null and alternative hypotheses? b) Given that a computer fails the test, what would you decide? What if it passes the test? c) How large is \(\alpha\) for this test? d) What is the power of this test? (Hint: How many possibilities are in the alternative hypothesis?)