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Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic failed to find evidence of a significant change compared with three years ago. Explain what the study's P-value of 0.17 means in this context.

A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using \(\alpha=0.05 .\) Would he have made the same decision at \(\alpha=0.10 ?\) How about \(\alpha=0.01 ?\) Explain.

Environmentalists concerned about the impact of high-frequency radio transmissions on birds found that there was no evidence of a higher mortality rate among hatchlings in nests near cell towers. They based this conclusion on a test using \(\alpha=0.05\). Would they have made the same decision at \(\alpha=0.10 ?\) How about \(\alpha=0.01 ?\) Explain.

Yahoo surveyed 2400 U.S. men. 1224 of the men identified themselves as the primary grocery shopper in their household. a. Estimate the percentage of all American males who identify themselves as the primary grocery shopper. Use a \(98 \%\) confidence interval. Check the conditions first. b. A grocery store owner believed that only \(45 \%\) of men are the primary grocery shopper for their family, and targets his advertising accordingly. He wishes to conduct a hypothesis test to see if the fraction is in fact higher than \(45 \% .\) What does your confidence interval indicate? c. What is the level of significance of this test? Explain.

Soon after the euro was introduced as currency in Europe, it was widely reported that someone had spun a euro coin 250 times and gotten heads 140 times. We wish to test a hypothesis about the fairness of spinning the coin. a. Estimate the true proportion of heads. Use a \(95 \%\) confidence interval. Don't forget to check the conditions. b. Does your confidence interval provide evidence that the coin is unfair when spun? Explain. c. What is the significance level of this test? Explain.

Canine hip dysplasia is a degenerative disease that causes pain in many dogs. Sometimes advanced warning signs appear in puppies as young as 6 months. A veterinarian checked 42 puppies whose owners brought them to a vaccination clinic, and she found 5 with early hip dysplasia. She considers this group to be a random sample of all puppies. a. Explain why we cannot use this information to construct a confidence interval for the rate of occurrence of early hip dysplasia among all 6 -month- old puppies. b. Could you use a bootstrap hypothesis test? Why or why not?

Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person's income level, credit history, current debt burden, and so on. The higher the point total, the more convinced the bank is that it's safe to make the loan. Any applicant with a lower point total than a certain cutoff score is denied a loan. We can think of this decision as a hypothesis test. Since the bank makes its profit from the interest collected on repaid loans, their null hypothesis is that the applicant will repay the loan and therefore should get the money. Only if the person's score falls below the minimum cutoff will the bank reject the null and deny the loan. This system is reasonably reliable, but, of course, sometimes there are mistakes. a. When a person defaults on a loan, which type of error did the bank make? b. Which kind of error is it when the bank misses an opportunity to make a loan to someone who would have repaid it? c. Suppose the bank decides to lower the cutoff score from 250 points to 200 . Is that analogous to choosing a higher or lower value of \(a\) for a hypothesis test? Explain. d. What impact does this change in the cutoff value have on the chance of each type of error?

Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message, and so on. The higher the point total, the more likely it is that the message is unwanted. The filter has a cutoff value for the point total; any message rated lower than that cutoff passes through to your inbox, and the rest, suspected to be spam, are diverted to the junk mailbox. We can think of the filter's decision as a hypothesis test. The null hypothesis is that the e-mail is a real message and should go to your inbox. A higher point total provides evidence that the message may be spam; when there's sufficient evidence, the filter rejects the null, classifying the message as junk. This usually works pretty well, but, of course, sometimes the filter makes a mistake. a. When the filter allows spam to slip through into your inbox, which kind of error is that? b. Which kind of error is it when a real message gets classified as junk? c. Some filters allow the user (that's you) to adjust the cutoff. Suppose your filter has a default cutoff of 50 points, but you reset it to 60 . Is that analogous to choosing a higher or lower value of \(\alpha\) for a hypothesis test? Explain. d. What impact does this change in the cutoff value have on the chance of each type of error?

In 2015 , the U.S. Census Bureau reported that \(62.2 \%\) of American families owned their homes the lowest rate in 20 years. Census data reveal that the ownership rate in one small city is much lower. The city council is debating a plan to offer tax breaks to first-time home buyers to encourage people to become homeowners. They decide to adopt the plan on a 2 -year trial basis and use the data they collect to make a decision about continuing the tax breaks. Since this plan costs the city tax revenues, they will continue to use it only if there is strong evidence that the rate of home ownership is increasing. a. In words, what will their hypotheses be? b. What would a Type I error be? c. What would a Type II error be? d. For each type of error, tell who would be harmed. e. What would the power of the test represent in this context?

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?