Problem Points 1 20 2 20 3 20 4 20 5 20 EC 10 Total 110 Name ________________________ Test #4 Math 150 / Fall 2012 / M. Zeitzew Show all work. One page notes both sides & calculator allowed. Don’t forget the rounding rules!!! ASSUME ALL POPULATIONS ARE NORMALLY DISTRIBUTED AND SIMPLE RANDOM SAMPLING IS DONE Before 200 174 198 170 179 182 193 209 185 155 169 210 After 191 170 177 167 159 151 176 183 159 145 146 177 Difference d= Before-After 1. Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after drug treatment, with the results given in the following table1. Use = 0.05 to test the claim that Captopril is effective at lowering systolic blood pressure. Use the traditional method. (HINT: these are dependent samples, so you’ll need statistics on the before/after differences) a. State the hypotheses and identify the claim H0: H1: b. Find the test statistic 1 Based on data from “Essential Hypertension: Effect of an Oral Inhibitor of Angiotensin-Converting Enzyme,” by MacGregor, et al., British Medical Journal, Vol. 2 c. Find the critical value(s) (& draw a picture to illustrate test statistic and critical value(s)) d. Make the decision (and explain why!) e. Summarize the results 2. Among 13,200 submitted abstracts that were blindly evaluated (with authors and institutions not identified), 26.7% were accepted for publication. Among 13,433 abstracts that were not blindly evaluated, 29.0% were accepted2. Use a 0.01 significance level to test the claim that the acceptance rate is the same with or without blinding. Use the P-Value method. a. State the hypotheses and identify the claim H0: H1: b. Find the test statistic c. Find the critical value(s) (& draw a picture to illustrate test statistic and critical value(s)) d. Make the decision (and explain why!) 2 Based on data from “Effect of Blinded Peer Review on Abstract Acceptance,” by Ross, et al., Journal of the American Medical Association, Vol. 295, No. 14 3. A simple random sample of 80 workers with high school diplomas is obtained, and the annual incomes have a mean of $37,622 and a standard deviation of $14,115. Another simple random sample of 39 workers with bachelor’s degrees is obtained, and the annual incomes have a mean of $77,689, with a standard deviation of $24,227. Use a 0.01 significance level to test the claim that the two samples are from populations with the same standard deviation. Use the traditional method a. State the hypotheses and identify the claim H0: H1: b. Find the test statistic c. Find the critical value(s) (& draw a picture to illustrate test statistic and critical value(s)) d. Make the decision (and explain why!) 4. Listed below are the numbers of deaths from lightning on the different days of the week. The deaths were recorded for a recent period of 35 years3. Use a 0.01 significance level to test the claim that deaths from lightning occur on the different days with the same frequency. Can you provide an explanation for the result? Use the Traditional method. Sunday Monday Tuesday Wednesday Thursday Friday Saturday Deaths 574 445 429 473 428 422 467 a. State the hypotheses and identify the claim H0: H1: b. Find the test statistic c. Find the critical value (& DRAW A PICTURE ILLUSTRATING TEST STATISTIC and critical value) d. Make the decision e. Summarize the results 3 Based on data from the National Oceanic and Atmospheric Administration 5. Find the best predicted quality score of a Hitachi television with a price of $1900. Is the predicted quality score close to the actual quality score of 56? Show your work or you will lose points. Price Quality Score 2300 1800 2500 2700 2000 1700 1500 2700 74 73 70 66 63 62 52 68 EXTRA CREDIT 6. Listed below are actual high temperatures and the high temperatures forecast five days in advance. a. First compute the differences between the actual and forecast highs and add them to the table. b. Perform the hypothesis test below. Use a 0.05 significance level with the sign test to test the claim that the population of differences has a median of zero. c. What do the results suggest about the accuracy of the forecasts? Actual High Forecast High 5 Days Earlier Difference 78 80 71 73 78 75 63 63 70 77 79 74 75 76 78 76 75 77 71 74 State the hypotheses and identify the claim H0: H1: Find the test statistic ??? Make the decision Summarize the results