You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 90% confidence, the proportion of people preferring Coke to within 5% of the actual value? Show all of your work.

reasoning for the latter is that the supervisor believes each proportion is around 3% to 5%, and the most conservative (largest) sample size corresponds to using the larger 5% value. Then the required sample size is 2.5?6 2 = 0.05 0.95 0.05 0.95 m 25,213 n (0-005) [ ( )+ ( )J This sample size (from each sample) is almost certainly prohibitive, so the supervisor real izes he must lower his goals. One way is to decrease the condence level, say, from 99% to 95%. Another way is to increase the desired half-length from 0.005 to, say, 0.025. We implemented both of these changes in Figure 8.19. Even now each required sample size is 584. Obviously, narrow condence intervals for differences between proportions can require very large sample sizes. I Figure 8. | 9 Sample Size for Difference Between Proportions a Sample Size for Difference of Proportions a Condence level 3 Ce nqage Learning