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Chapter 9: Q.11.47 (page 460)
A sample size that will ensure a margin of error of at most the one specified.
The required sample size is 1, 842
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Does Aspirin Prevent Heart Disease? In a trial designed to test the effectiveness of aspirin in preventing heart disease, 11,037 male physicians were treated with aspirin and 11,034 male physicians were given placebos. Among the subjects in the aspirin treatment group, 139 experienced myocardial infarctions (heart attacks). Among the subjects given placebos, 239 experienced myocardial infarctions (based on data from 鈥淔inal Report on the Aspirin Component of the Ongoing Physicians鈥� Health Study,鈥� New England Journal of Medicine, Vol. 321: 129鈥�135). Use a 0.05 significance level to test the claim that aspirin has no effect on myocardial infarctions.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, does aspirin appear to be effective?
Testing Claims About Proportions. In Exercises 7鈥�22, 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.
Cell Phones and Handedness A study was conducted to investigate the association between cell phone use and hemispheric brain dominance. Among 216 subjects who prefer to use their left ear for cell phones, 166 were right-handed. Among 452 subjects who prefer to use their right ear for cell phones, 436 were right-handed (based on data from 鈥淗emi- spheric Dominance and Cell Phone Use,鈥� by Seidman et al., JAMA Otolaryngology鈥擧ead & Neck Surgery, Vol. 139, No. 5). We want to use a 0.01 significance level to test the claim that the rate of right-handedness for those who prefer to use their left ear for cell phones is less than the rate of right-handedness for those who prefer to use their right ear for cell phones. (Try not to get too confused here.)
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
Degrees of FreedomIn Exercise 20 鈥淏lanking Out on Tests,鈥� using the 鈥渟maller of\({n_1} - 1\) and \({n_2} - 1\)鈥� for the number of degrees of freedom results in df = 15. Find the number of degrees of freedom using Formula 9-1. In general, how are hypothesis tests and confidence intervals affected by using Formula 9-1 instead of the 鈥渟maller of \({n_1} - 1\)and \({n_2} - 1\)鈥�?
Braking Reaction Times: Normal? The accompanying normal quantile plot is obtained by using the braking reaction times of females listed in Exercise 6. Interpret this graph.
Verifying requirements in the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group considered of 201,229 children given the sulk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those children developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the sulk vaccine, are the requirements for a hypothesis test satisfied? Explain.
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