456 Chapter 9 Hypothesis Testing said that they had a great deal of confidence. An economist claims that less than 15% of U.S. adults have a great deal of confidence in banks. a. State the appropriate null and alternate hypotheses. H0 : p = 0.15, H1: p < 0.15 b. Compute the test statistic z. −3.83 c. Using �� = 0.05, can you conclude that the executive’s claim is true? Yes d. Using �� = 0.01, can you conclude that the executive’s claim is true? Yes 15. Kids with cell phones: A marketing manager for a cell phone company claims that more than 55% of children aged 8–12 have cell phones. In a 2012 survey of 802 children aged 8–12 by the National Consumers League, 449 of them had cell phones. Can you conclude that the manager’s claim is true? Use the �� = 0.01 level of significance. Do not reject H0. 16. Internet tax: In 2013, the Gallup Poll asked 1015 U.S. adults whether they believed that people should pay sales tax on items purchased over the Internet. Of these, 437 said they supported such a tax. Does the survey provide convincing evidence that less than 45% of U.S. adults favor an Internet sales tax? Use the �� = 0.05 level of significance. Do not reject H0. 17. Quit smoking: In a survey of 444 HIV-positive smokers, 170 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine patch? Use the �� = 0.05 level of significance. Reject H0. Source: American Journal of Health Behavior 32:3–15 18. Game consoles: A poll taken by the Software Usability Research Laboratory in 2012 surveyed 341 video gamers, and 110 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that more than 25% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the �� = 0.01 level of significance. Reject H0. 19. Tattoo: A Harris poll taken in 2012 surveyed 2016 adults and found that 423 of them had one or more tattoos. Can you conclude that the percentage of adults who have a tattoo is less than 25%? Use the �� = 0.01 level of significance. Reject H0. 20. Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that more than 60% of those with diabetes who undergo this surgery will recover from diabetes? Use the �� = 0.05 level of significance. Reject H0. Source: New England Journal of Medicine 357:753–761 21. Tweet tweet: An article in Forbes magazine in December 2012 reported that 73% of Fortune 500 companies have Twitter accounts. A economist thinks the percentage is higher at technology companies. She samples 70 technology companies and finds that 55 of them have Twitter accounts. Can she conclude that more than 73% of technology companies have Twitter accounts? Use the �� = 0.05 level of significance. Do not reject H0. 22. Online photos: A Pew poll taken in December 2012 surveyed 1802 Internet users and found that 829 of them had posted a photo or video online. Can you conclude that less than half of Internet users have posted photos or videos online? Use the �� = 0.05 level of significance. Reject H0. 23. Choosing a doctor: Which do patients value more when choosing a doctor: interpersonal skills or technical ability? In a recent study, 304 people were asked to choose a physician based on two hypothetical descriptions. One physician was described as having high technical skills and average interpersonal skills, and the other was described as having average technical skills and high interpersonal skills. The physician with high interpersonal skills was chosen by 116 of the people. Can you conclude that less than half of patients prefer a physician with high interpersonal skills? Use the �� = 0.01 level of significance. Reject H0. Source: Health Services Research 40:957–977 24. Cable TV choices: A telecommunications company provided its cable TV subscribers with free access to a new sports channel for a period of one month. It then chose a sample of 400 television viewers and asked them whether they would be willing to pay an extra $10 per month to continue to access the channel. A total of 25 of the 400 replied that they would be willing to pay. The marketing director of the company claims that more than 5% of all its subscribers would pay for the channel. Can you conclude that the director’s claim is true? Use the �� = 0.01 level of significance. Do not reject H0. 25. Interpret calculator display: The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion p. a. What are the null and alternate hypotheses? b. What is the value of the sample proportion ̂p? 0.3382352941 c. Can H0 be rejected at the 0.05 level? Explain. Yes d. Someone wants to use these data to test H0 : p = 0.25 versus H1: p ≠ 0.25. Find the test statistic z and use the method of this section to find the P-value. Do you reject H0 at the �� = 0.05 level? 1.68; no 26. Interpret calculator display: The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion p.
navidi_monk_elementary_statistics_2e_ch7-9
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