7.4 EXERCISES SECTION 7.4 Hypothesis Testing for Proportions 391 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Explain how to determine whether a normal distribution can be used to approximate a binomial distribution. 2. Explain how to test a population proportion p. In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim. 3. Claim: p 6 0.12; a = 0.01. Sample statistics: np = 0.10, n = 40 4. Claim: p Ú 0.48; a = 0.08. Sample statistics: np = 0.40, n = 90 5. Claim: p ≠ 0.15; a = 0.05. Sample statistics: np = 0.12, n = 500 6. Claim: p 7 0.70; a = 0.04. Sample statistics: np = 0.64, n = 225 Using and Interpreting Concepts Hypothesis Testing Using Rejection Regions In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. 7. School Vaccinations Prior to COVID-19, a reporter claims that more than 80% of U.S. adults feel children should be vaccinated to attend school. In a random sample of 200 U.S. adults, 84% feel that children should be vaccinated to attend school. At a = 0.01, can you support the reporter’s claim? (Adapted from Harvard T.H. Chan School of Public Health) 8. Vaccinations In 2021, a reporter claims that at least 55% of U.S. adults feel that COVID-19 vaccinations should be required for high school students to attend school in the fall. In a random sample of 200 U.S. adults, 56% feel that COVID-19 vaccinations should be required for high school students to attend school in the fall. At a = 0.10, is there enough evidence to reject the reporter’s claim? (Adapted from Gallup) 9. Tax Refunds A tax analyst says that at least 60% of tax filers are expecting a tax refund. In a random sample of 2494 U.S. tax filers, 56% are expecting a tax refund. At a = 0.05, is there enough evidence to reject the analyst’s claim? (Adapted from CreditCards.com) 10. Working Students An education researcher claims that 65% of full-time college students work year-round. In a random sample of 105 college students, 66 say they work year-round. At a = 0.10, is there enough evidence to reject the researcher’s claim? (Adapted from Student Loan Hero) 11. Nursing A patient care manager claims that more than half of all nurses feel they became better professionals during the coronavirus pandemic. In a random sample of 300 nurses, 174 say they became better professionals during the pandemic. At a = 0.01, is there enough evidence to support the manager’s claim? (Adapted from University of Phoenix) 12. Changing Jobs A researcher claims that 40% of U.S. adults would consider changing jobs. In a random sample of 50 U.S. adults, 25 say they would consider changing jobs. At a = 0.10, is there enough evidence to reject the researcher’s claim? (Adapted from CBS News)
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