6.3 EXERCISES SECTION 6.3 Confidence Intervals for Population Proportions 325 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary True or False? In Exercises 1 and 2, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 1. The point estimate for the population proportion of failures is 1 - np. 2. To find the minimum sample size required for a confidence interval, solve for n in the formula for margin of error and round to the nearest whole number. Finding np and nq In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q. 3. Tax Fraud In a survey of 1040 U.S. adults, 62 have had someone impersonate them to try to claim tax refunds. (Adapted from Pew Research Center) 4. Social Security In a survey of 351 retired Americans, 200 said that they rely on Social Security as major source of income. (Adapted from Gallup) 5. Social Security In a survey of 661 non-retired Americans, 218 said that they expect to rely on Social Security as major source of income when they retire. (Adapted from Gallup) 6. Private Internet Browsing In a survey of 4272 U.S. adults, 1025 knew that private browsing mode only prevents someone using the same computer from seeing one’s online activities. (Adapted from Pew Research Center) In Exercises 7–10, use the confidence interval to find the margin of error and the sample proportion. 7. (0.905, 0.933) 8. (0.245, 0.475) 9. (0.512, 0.596) 10. (0.087, 0.263) Using and Interpreting Concepts Constructing Confidence Intervals In Exercises 11 and 12, construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. 11. New Year’s Resolutions In a survey of 1790 U.S. adults in a recent year, 1325 say they have a New Year’s resolution. (Adapted from Finder) 12. New Year’s Resolutions In a survey of 1790 U.S. adults in a recent year, 816 have a New Year’s resolution related to their health. (Adapted from Finder) Constructing Confidence Intervals In Exercises 13 and 14, construct a 99% confidence interval for the population proportion. Interpret the results. 13. Terrorism In a survey of 1010 U.S. adults, 364 said that they worry a great deal about the possibility of a future terrorist attack. (Adapted from Gallup) 14. Hunger and Homelessness In a survey of 1010 U.S. adults, 556 said that they worry a great deal about hunger and homelessness. (Adapted from Gallup)
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