Math215 - Statistical Concepts Names: _______________________________ Suppose the coach of the football team wants to estimate the proportion of the population of fans who support his current starter lineup. The coach wants the estimate to be .04 of the true proportion. Assume a 99 percent level of confidence. The coach estimated the proportion supporting the current starter lineup to be .60. Answer the following questions: 1. Construct a 99% confidence interval using a sample size of 50, then of 100, then of 1,000. 2. How did changing the sample size affect the size of the interval? The larger the sample size, the smaller the size of the interval. 3. What is the error of the estimate for each of these sample sizes? 4. How large of a sample is required for the error of the estimate to be within +.04 of the population proportion? 5. How large would the sample have to be if the coach of the team were not available? Show your work. Be prepared to present your analysis to the class. Part II. In a study designed to test the effectiveness of acupuncture for treating migraine, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The numbers of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2. 1. Construct an 85% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture. 2. Interpret this interval in the context of this problem. 3. Construct an 85% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment. 4. Interpret this interval in the context of this problem. 5. Compare the two confidence intervals. Do the results suggest the effectiveness of one method over the other? 1 130314