444 Chapter 9 Hypothesis Testing c. �� = 0.10, n = 16, H1: �� ≠ ��0 −1.753, 1.753 d. �� = 0.05, n = 11, H1: �� < ��0 −1.812 14. Find the critical value or values for the following values of the significance level ��, sample size n, and alternate hypothesis H1. a. �� = 0.05, n = 39, H1: �� > ��0 1.686 b. �� = 0.01, n = 34, H1: �� < ��0 −2.445 c. �� = 0.10, n = 6, H1: �� ≠ ��0 −2.015, 2.015 d. �� = 0.05, n = 25, H1: �� ≠ ��0 −2.064, 2.064 Working with the Concepts 15. Is there a doctor in the house? The market research firm Salary.com reported that in June of 2013, the mean annual earnings of all family practitioners in the United States was $178,258. A random sample of 55 family practitioners in Los Angeles that month had mean earnings of ̄x = $192,340 with a standard deviation of $42,387. Do the data provide sufficient evidence to conclude that the mean salary for family practitioners in Los Angeles is greater than the national average? a. State the null and alternate hypotheses. H0 : �� = 178,258, H1: �� > 178,258 b. Compute the value of the t statistic. How many degrees of freedom are there? 2.464; 54 degrees of freedom c. State your conclusion. Use the �� = 0.05 level of significance. Reject H0. 16. College tuition: The mean annual tuition and fees in the 2013–2014 academic year for a sample of 14 private colleges in California was $37,900 with a standard deviation of $7,200. A dotplot shows that it is reasonable to assume that the population is approximately normal. Can you conclude that the mean tuition and fees for private institutions in California differs from $35,000? a. State the null and alternate hypotheses. H0 : �� = 35,000, H1: �� ≠ 35,000 b. Compute the value of the t statistic. How many degrees of freedom are there? 1.507; 13 degrees of freedom c. State your conclusion. Use the �� = 0.01 level of significance. Do not reject H0. Based on data from collegeprowler.com 17. Big babies: The National Health Statistics Reports described a study in which a sample of 360 one-year-old baby boys were weighed. Their mean weight was 25.5 pounds with standard deviation 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds. Do the data provide convincing evidence that the pediatrician’s claim is true? Use the �� = 0.01 level of significance. Do not reject H0. 18. Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO score is lower than the cutoff of 720. She finds that a random sample of 100 people had a mean FICO score of 703 with a standard deviation of 92. Can the economist conclude that the mean FICO score is less than 720? Use the �� = 0.05 level of significance. Reject H0. 19. Commuting to work: The 2011 American Community Survey sampled 1923 people in Colorado and asked them how long it took them to commute to work each day. The sample mean one-way commute time was 24.5 minutes with a standard deviation of 13.0 minutes. A transportation engineer claims that the mean commute time is less than 25 minutes. Do the data provide convincing evidence that the engineer’s claim is true? Use the �� = 0.05 level of significance. Reject H0. 20. Watching TV: In 2012, the General Social Survey asked a sample of 1298 people how much time they spent watching TV each day. The mean number of hours was 3.09 with a standard deviation of 2.87. A sociologist claims that people watch a mean of 3 hours of TV per day. Do the data provide sufficient evidence to disprove the claim? Use the �� = 0.01 level of significance. Do not reject H0. 21. Weight loss: In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 14 people, based on means and standard deviations given in the article. 18.2 24.8 3.9 20.0 17.1 8.8 13.4 17.3 33.8 29.7 8.5 31.2 19.3 15.1 Source: Journal of the American Medical Association 299:1139–1148 a. Following is a boxplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain. Yes 0 10 20 30 40 b. If appropriate, perform a hypothesis test to determine whether the mean weight loss is greater than 10 pounds. Use the �� = 0.05 level of significance. What do you conclude? Reject H0. 22. How much is in that can? A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans. 11.96 12.10 12.04 12.13 11.98 12.05 11.91 12.03 a. Following is a dotplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain. Yes
navidi_monk_elementary_statistics_2e_ch7-9
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