Chapter 7, Problem 61SE

Marijuana Legalization A 2017 Gallup poll reported that 658 out of 1028 U.S. adults believe that marijuana should be legalized. When Gallup first polled U.S. adults about this subject in 1969, only $12\%$ supported legalization. Assume the conditions for using the CLT are met.

a. Find and interpret a $99\%$ confidence interval for the proportion of U.S. adults in 2017 that believe marijuana should be legalized.

b. Find and interpret a $95\%$ confidence interval for this population parameter.

c. Find the margin of error for each of the confidence intervals found in parts $a\text{ and }b.$

d. Without computing it, how would the margin of error of a $90\%$ confidence interval compare with the margin of error for the $95\%$ and $99\%$ intervals? Construct the $90\%$ confidence interval to see if your prediction was correct.