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 (to 4 decimals). Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.)
Government industry
Health care industry
Education industry
b. Assuming the sample size will be the same 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? (Round sample size (n) up to the next integer value.)
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