446 Chapter 9 Hypothesis Testing h. Can the null hypothesis in part (f) be rejected at the 0.05 level? Explain. No 30. Interpret calculator display: The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean ��. a. State the null and alternate hypotheses. H0 : �� = 20, H1: �� ≠ 20 b. What is the value of ̄x? 20.75 c. What is the value of s? 3.93 d. How many degrees of freedom are there? 39 e. Do you reject H0 at the 0.05 level? Explain. No f. Someone wants to test the hypothesis H0 : �� = 22.5 versus H1: �� ≠ 22.5. Use the information in the display to compute the t statistic for this test. −2.816 g. Compute the P-value for this test. h. Can the null hypothesis in part (f) be rejected at the 0.05 level? Explain. Yes 31. Interpret computer output: The following computer output (from MINITAB) presents the results of a hypothesis test for a population mean ��. �������� ���� ���� = �� �� ���� > �� �� �� �� �� �� ���� �� �������� ���������� ���� �������� ����% ���������� ���������� �� ���������� ������������ ������������ �������� �� ���������� a. State the null and alternate hypotheses. H0 : �� = 5.5, H1: �� > 5.5 b. What is the value of ̄x? 5.92563 c. What is the value of s? 0.15755 d. How many degrees of freedom are there? 4 e. Do you reject H0 at the 0.05 level? Explain. Yes f. Someone wants to test the hypothesis H0 : �� = 6.5 versus H1: �� < 6.5. Use the information in the output to compute the t statistic for this test. −8.152 g. Compute the P-value for this test. 0.00062 h. Can the null hypothesis in part (f) be rejected at the 0.05 level? Explain. Yes 32. Interpret computer output: The following computer output (from MINITAB) presents the results of a hypothesis test for a population mean ��. �������� ���� ���� = ���� ���� ������ = ���� �� *�� ���� �� �� ������ �� �������� ���� ������������ ���������� �� �������� ���� �������� �� �������� ����~ ���� .�� ��������, ���� �������� / a. State the null and alternate hypotheses. H0 : �� = 16, H1: �� ≠ 16 b. What is the value of ̄x? 13.2874 c. What is the value of s? 6.0989 d. How many degrees of freedom are there? 10 e. Do you reject H0 at the 0.05 level? Explain. No f. Someone wants to test the hypothesis H0 : �� = 9 versus H1: �� > 9. Use the information in the output to compute the t statistic for this test. 2.332 g. Compute the P-value for this test. 0.0210 h. Can the null hypothesis in part (f) be rejected at the 0.05 level? Explain. Yes 33. Does this diet work? In a study of the effectiveness of a certain diet, 100 subjects went on the diet for a period of six months. The sample mean weight loss was 0.5 pound, with a sample standard deviation of 4 pounds. a. Find the t statistic for testing H0 : �� = 0 versus H1: �� > 0. 1.25 b. Find the P-value for testing H0 : �� = 0 versus H1: �� > 0. 0.1071 c. Can you conclude that the diet produces a mean weight loss that is greater than 0? Use the �� = 0.05 level of significance. No 34. Effect of larger sample size: The study described in Exercise 33 is repeated with a larger sample of 1000 subjects. Assume that the sample mean is once again 0.5 pound and the sample standard deviation is once again 4 pounds. a. Find the t statistic for testing H0 : �� = 0 versus H1: �� > 0. Is the value of the t statistic greater than or less than the value obtained with a smaller sample of 100? 3.953; larger b. Find the P-value for testing H0 : �� = 0 versus H1: �� > 0. 0.000041 c. Can you conclude that the diet produces a mean weight loss that is greater than 0? Use the �� = 0.05 level of significance. Yes d. Explain why the mean weight loss is not of practical significance, even though the results are statistically significant at the 0.05 level. 35. Perform a hypothesis test? A sociologist wants to test the null hypothesis that the mean number of people per household in a given city is equal to 3. He surveys 50 households on a certain block in the city and finds that the sample mean number of people is 3.4 with a standard deviation of 1.2. Should these data be used to perform a hypothesis test? Explain why or why not. No 36. Perform a hypothesis test? A health professional wants to test the null hypothesis that the mean length of hospital stay for a certain surgical procedure is 4 days. She obtains records for all the patients who have undergone the procedure at a certain hospital during a given year, and finds that the mean length of stay is 4.7 days with a standard deviation of 1.1 days. Should these data be used to perform a hypothesis test? Explain why or why not. No 37. Larger or smaller P-value? In a study of sleeping habits, a researcher wants to test the null hypothesis that adults in a certain community get a mean of 8 hours of sleep versus the alternative that the mean is not equal to 8. In a sample of 250 adults, the mean number of hours of sleep was 8.2. A second researcher repeated the study with a different sample of 250, and obtained a sample mean of 7.5. Both researchers obtained the same standard deviation. Will the P-value of the second researcher be greater than or less than that of the first researcher? Explain. less 38. Larger or smaller P-value? Juan and Mary want to test the null hypothesis that the mean length of text messages sent by students at their school is 10 characters versus the alternative that it is less. Juan samples 100 text messages and finds the mean length to be 8.4 characters. Mary
navidi_monk_elementary_statistics_2e_ch7-9
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