Th e 2011 Statistical Abstract of the United States includes a table reporting that a national survey in the fall of 2009 found that 18.2% of American adults played a board game in the past year. We can use this sample result to estimate the proportion of all adult Americans who had played a board game in the past year.
a. What additional information do you need in order to determine a 95% confidence interval for the probability that a randomly selected American adult had played a board game in the past year?
b. Consider three possible sample sizes for this study: 250, 1,000, and 4,000. Without performing any calculations, how do you expect three confidence intervals based on these sample sizes to compare to each other? Explain your reasoning.
c. Carry out the simulation at each sample size to get the SD and use the 2SD method to approximate the margin of error with each of these three sample sizes. Th en produce the 95% confidence interval for each of these three sample sizes.
d. How do the midpoints of these intervals compare?
e. How do the widths of these intervals compare?
f. By how many times must the sample size increase in order to cut the margin of error in half?

g. Suppose that the sample size was really 1,000. Based on the confidence interval, do the sample data suggest that fewer than 25% of all adult Americans had played a board game in the past year?