7-1 Estimating a Population Proportion 327 24. Job Interviews In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. a. Among the 514 human resource professionals who were surveyed, how many of them said that the appearance of a job applicant is most important for a good first impression? b. Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression. c. Repeat part (b) using a confidence level of 80%. d. Compare the confidence intervals from parts (b) and (c) and identify the interval that is wider. Why is it wider? 25. Really Large Sample A Quest Diagnostics analysis of 10 million drug tests revealed that 4.2% of them tested positive for illegal drugs. Construct a 95% confidence interval estimate of the positive test rate, and construct a 99% confidence interval estimate of that rate. Comment on the results. 26. Gender Selection Before its clinical trials were discontinued, the Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl and, among the 945 babies born to parents using the XSORT method, there were 879 girls. The YSORT method was designed to increase the probability of conceiving a boy and, among the 291 babies born to parents using the YSORT method, there were 239 boys. Construct the two 95% confidence interval estimates of the percentages of success. Compare the results. What do you conclude? 27. 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. Among 199 patients given standard care, 62.8% 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). Construct the two 95% confidence interval estimates of the percentages of success. Compare the results. What do you conclude? 28. Measured Results vs. Reported Results The same study cited in the preceding exercise produced these results after six months for the 198 patients given sustained care: 25.8% were no longer smoking, and these results were biochemically confirmed, but 40.9% of these patients reported that they were no longer smoking. Construct the two 95% confidence intervals. Compare the results. What do you conclude? Using Appendix B Data Sets. In Exercises 29 and 30, use the indicated data set in Appendix B. 29. Heights of Presidents Refer to Data Set 22 “Presidents” in Appendix B. Treat the data as a sample and find the proportion of presidents who were taller than their opponents. Use that result to construct a 95% confidence interval estimate of the population percentage. Based on the result, does it appear that greater height is an advantage for presidential candidates? Why or why not? 30. Green M&Ms Data Set 38 “Candies” in Appendix B includes data from 345 M&M plain candies, and 53 of them are green. The Mars candy company claims that 16% of its M&M plain candies are green. Use the sample data to construct a 95% confidence interval estimate of the percentage of green M&Ms. What do you conclude about the claim of 16%? Determining Sample Size. In Exercises 31–38, use the given data to find the minimum sample size required to estimate a population proportion or percentage. 31. Wiggle Your Ears Find the sample size needed to estimate the percentage of adults who can wiggle their ears. Use a margin of error of 3 percentage points and use a confidence level of 99%. continued
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