8-2 Testing a Claim About a Proportion 401 Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. 9. Cursed Movie Released in 1956, the movie The Conqueror attracted considerable attention because many members of the cast and crew died from cancer supposedly resulting from exposure to radioactive fallout. The movie was shot a short distance from a site in Nevada where above-ground tests of atomic weapons were conducted. Among the 220 cast and crew members, 91 developed cancer. According to the National Cancer Institute, for that time period and for the age cohort, the incidence of cancer was about 40%. Use a 0.05 significance level to test the claim that the sample of cast and crew members is from a population in which the rate of cancer is greater than 40%. What do you conclude about the movie being a curse? 10. MythBusters The Discovery channel television show MythBusters conducted an experiment to study what happens when buttered toast is dropped on the floor. When 48 buttered slices of toast were dropped, 29 of them landed with the buttered side up and 19 landed with the buttered side down. Use a 0.05 significance level to test the claim that toast will land with the buttered side down 50% of the time. Write a conclusion that addresses the intent of the experiment. 11. Clothing Care Instructions For clothing, the accompanying symbol has been designated to indicate that the product should be dry-cleaned only. In a survey of 2005 Americans, 11% correctly knew what the symbol designated. Use a 0.01 significance level to test the claim that fewer than half of all Americans know what the symbol designates. What do these results suggest about this symbol? 12. M&Ms Data Set 38 “Candies” in Appendix B lists data from 345 M&Ms, and 25.5% of them are blue. The Mars candy company claims that the percentage of blue M&Ms is equal to 24%. Use a 0.05 significance level to test that claim. Should Mars take corrective action? 13. OxyContin The drug OxyContin (oxycodone) is used to treat pain, but it is dangerous because it is addictive and can be lethal. In clinical trials, 227 subjects were treated with OxyContin and 52 of them developed nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test the claim that more than 20% of OxyContin users develop nausea. Does the rate of nausea appear to be too high? 14. Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. Should this be comforting to physicians? 15. News Media A Pew Research Center poll of 4581 Americans showed that 47% of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.01 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. 16. Internet Use A random sample of 5005 adults in the United States includes 751 who do not use the Internet (based on three Pew Research Center polls). Use a 0.05 significance level to test the claim that the percentage of U.S. adults who do not use the Internet is now less than 48%, which was the percentage in the year 2000. If there appears to be a difference, is it dramatic? 17. Births A random sample of 860 births in New York State included 426 boys. Use a 0.05 significance level to test the claim that 51.2% of newborn babies are boys. Do the results support the belief that 51.2% of newborn babies are boys?
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