Workers in several industries were surveyed to determine the proportion of workers who feel their industry is understaffed. In the government sector, 37% of the respondents said they were understaffed, in the health care sector 33% said they were understaffed, and in the education sector 28% said they were understaffed (USA today, January 11, 2010). Suppose that 200 workers were surveyed in each industry.

a. Construct a 95% confidence interval for the proportion of workers in each of these industries who feel their industry is understaffed.

b. Assuming the same sample size will be used in each industry, 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?