91Ó°ÊÓ

Write the null and alternative hypotheses you would use to test each of the following situations: a) A governor is concerned about his "negatives" - -the percentage of state residents who express disapproval of his job performance. His political committee pays for a series of TV ads, hoping that they can keep the negatives below \(30 \% .\) They will use follow-up polling to assess the ads' effectiveness. b) Is a coin fair? c) Only about \(20 \%\) of people who try to quit smoking succeed. Sellers of a motivational tape claim that listening to the recorded messages can help people quit.

b) \(20 \%\) of cars of a certain model have needed costly transmission work after being driven between 50,000 and 100,000 miles. The manufacturer hopes that a redesign of a transmission component has solved this problem. c) We field-test a new-flavor soft drink, planning to market it only if we are sure that over \(60 \%\) of the people like the flavor. Write the null and alternative hypotheses you would use to test each situation. a) In the 1950 s only about \(40 \%\) of high school graduates went on to college. Has the percentage changed?

Someone hands you a box of a dozen chocolate covered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla. a) If there really were 6 vanilla and 6 peanut butter candies in the box, what is the probability that you would have picked three vanillas in a row? b) Do you think there really might have been 6 of each? Explain. c) Would you continue to believe that half are vanilla if the fourth one you try is also vanilla? Explain.

A very large study showed that aspirin reduced the rate of first heart attacks by \(44 \% . \mathrm{A}\) pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. a) What is the null hypothesis the company will use? b) What is their alternative hypothesis? They conducted the study and found that the group using the new drug had somewhat fewer heart attacks than those in the aspirin group. c) The P-value from the hypothesis test was 0.28. What do you conclude? d) What would you have concluded if the P-value had been 0.004?

A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or spades), without looking, of course! a) State the null hypothesis for your experiment. b) State the alternative hypothesis. You did the experiment and your friend correctly identified more than \(25 \%\) of the cards. c) A hypothesis test gave a P-value of 0.014. What do you conclude? d) What would you conclude if the P-value had been \(0.245 ?\)

A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than \(20 \%\) of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Like a lot of other Americans, John Wayne died of cancer. But is there more to this story? In 1955 Wayne was in Utah shooting the film The Conqueror. Across the state line, in Nevada, the United States military was testing atomic bombs. Radioactive fallout from those tests drifted across the filming location. A total of 46 of the 220 people working on the film eventually died of cancer. Cancer experts estimate that one would expect only about 30 cancer deaths in a group this size. a) Is the death rate among the movie crew unusually high? b) Does this prove that exposure to radiation increases the risk of cancer?