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Chapter 7 Part 1 (Confidence Interval Estimate for p // Hypothesis Testing Concerning p) Use the following information to answer questions 1-3. An investigator wishes to estimate the proportion of Type II diabetic patients who take insulin to manage their diabetes. A large, national database of Type II diabetic patients is used to generate the estimate. The database involves a random sample of 1200 Type II diabetic patients, 423 of whom report taking insulin to manage their diabetes. 1. Compute a point estimate for the proportion of all Type II diabetics who take insulin to manage their diabetes. a. p =423 b. p =0.35 c. p =1200 d. p =2.84 2. Compute the standard error of the point estimate. (Remember the standard error of the point estimate is the same as the standard deviation of the point estimate ( p ). 6, =0.35 b. o; =0.32 c. 6; =0.38 d. 6) =0.014 3. Compute a 95% confidence interval for the proportion of all Type II diabetics who take insulin to manage their diabetes. a. (0.350, 0.370) b. (0.323 , 0.377) c. (-1.96, 1.96) d. (0.370, 0.350) 4. Suppose we wish to estimate what proportion of patients in an HMO spend more than $500 on prescription medications over 12 months. In a random sample of 150 patients, 34% spent more than $500. Construct a 90% confidence interval for the true proportion of patients who spend more than $500 on prescription medications per year. a. (0.276, 0.404) b. (0.34 , 0.36) c. (-1.645, 1.645) d. (0.36, 0.34) Use the following information to answer questions 5-8. A national study reports that 28% of high school students smoke. We wish to test if the smoking rate is higher than the national rate among freshmen at a local university. To run the test, we take a random sample of 200 freshmen, and 32% report that they smoke. Run the appropriate test at a 5% level of significance. 5. State the null and alternative hypothesis. a. Ho: p = 0.28 HI: p > 0.28 b. Ho: p = 0.32 HI: p> 0.32 c. Ho: p = 0.28 HI: p50.28 d. Ho: p = 0.28 HI: p # 0.28 6. What is the critical value of the test and your decision rule? a. 1.96; Reject Ho if the test statistic is greater than or equal to 1.96, otherwise not enough evidence to reject Ho. b. 1.26; Reject Ho if the test statistic is greater than or equal to 1.26, otherwise not enough evidence to reject Ho. C. 1.645 Reject Ho if the test statistic is greater than or equal to 1.645, otherwise not enough evidence to reject Ho. d. -1.26; Reject Ho if the test statistic is greater than or equal to - 1.26, otherwise not enough evidence to reject Ho. 7. What is the test statistic? a. 1.96 b. 1.26 C. 1.645 d -1.26 8. State your conclusion. a. Reject Ho: there is significant evidence ( a = 0.05) that the smoking rate among freshmen a local university is greater than the national rate. b. Not enough evidence to reject Ho: there is NOT significant evidence ( a = 0.05) that the smoking rate among freshmen at this local university is greater than the national rate
