11. A polling agency wants to predict the the percentage of votes candidate A will receive in election day. Their objective is that the difference between the estimate and the actual fraction of votes candidate A will receive should not exceed a half percent, with 95% prob- ability. How large sample should they draw from the population in order to achieve this objective? 14. A polling agency collected data concerning a coming election. They polled 100 voters. In this sample 56 people said that they will vote for candidate A. Create a 95% confidence interval for the proportion of votes candidate A will receive in the election. 15. A manufacturer of boxes of candy is concerned about the proportion of imperfect boxes - those containing cracked, broken, or otherwise damaged candies. (a) How large a sample is needed to be 99% confident that the difference between the sample fraction of imperfect boxes and the population proportion of imperfect boxes is no more than .015? Assume here that we have absolutely no information concerning the true proportion of imperfect boxes. (b) How does your answer to part (a) change if we assume that the population proportion of imperfect boxes is at least .005 and no more than .1?