The American Enterprise Institute (AEI) Public Opinion Study found that 86% of Americans are satisfied with their job (AEI website, December 4, 2015). Is this consistent across age groups? A follow-up survey revealed that 72% of Americans age 18-30 are satisfied with their job, 85% of Americans age 31-50 are satisfied with their job, and 93% of Americans age 51-70 are satisfied with their job. Suppose that 200 workers were surveyed in each age group.
a. Construct a 95% confidence interval for the proportion of workers in each of these age groups who is satisfied with her or his job. Do these results surprise you? Why or why not?
b. Assuming the same sample size will be used in each age group, how large would the sample need to be to ensure that the margin of error is .05 or less for each of the three confidence intervals?