Suppose that Nabisco would like to determine, with 95% confidence and a maximum likely error of 0.03, the proportion of first graders in Pennsylvania who had Nabisco's Spoon-Size Shredded Wheat for breakfast at least once last week. In determining the necessary size of a simple random sample for this purpose:
a. Use 0.5 as your estimate of the population proportion.
b. Do you think the population proportion could really be as high as 0.5? If not, repeat part (a) using an estimated proportion that you think would be more likely to be true. What effect does your use of this estimate have on the sample size?