8-2 Testing a Claim About a Proportion 403 28.Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone death to survive a major holiday or important event such as a birthday. In a study, it was found that there were 6062 deaths in the week before Thanksgiving, and 5938 deaths the week after Thanksgiving (based on data from “Holidays, Birthdays, and Postponement of Cancer Death,” by Young and Hade, Journal of the American Medical Association, Vol. 292, No. 24). If people can postpone death until after Thanksgiving, then the proportion of deaths in the week before should be less than 0.5. Use a 0.05 significance level to test the claim that the proportion of deaths in the week before Thanksgiving is less than 0.5. Based on the result, does there appear to be any indication that people can temporarily postpone death to survive the Thanksgiving holiday? 29.Belief in Ghosts In a Harris Interactive poll of 2250 adults, 42% of the respondents said that they believe in ghosts. Use a 0.01 significance level to test the claim that more than 1>3 of adults believe in ghosts. 30.Smoking Stopped In a program designed to help patients stop smoking, 198 patients were given sustained care, and 82.8% of them were no longer smoking after one month (based on data from “Sustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,” by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). Use a 0.01 significance level to test the claim that 80% of patients stop smoking when given sustained care. Does sustained care appear to be effective? 31.Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. Use a 0.01 significance level to test the claim that the selection process is biased against Americans of Mexican ancestry. Does the jury selection system appear to be biased? 32.Legalization of Marijuana In 1969, only 12% of Americans were in favor of legalizing marijuana. A recent Pew Research Center poll of 1201 adults showed that 57% of them supported the legalization of marijuana. Use a 0.01 significance level to test the claim that the current rate of support is greater than the 12% level in 1969. 33.Exact Method For each of the three different methods of hypothesis testing (identified in the left column), enter the P-values corresponding to the given alternative hypothesis and sample data. Use a 0.05 significance level. Note that the entries in the last column correspond to the Chapter Problem. How do the results agree with the large sample size? H1: p 3 0.5 n = 10, x = 9 H1: p 3 0.4 n = 10, x = 9 H1: p + 0.5 n = 926, x = 482 Normal approximation Exact Exact with simple continuity correction 34.Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1. a. Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1. b. Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1. 8-2 Beyond the Basics continued
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