Suppose the Akron Chamber of Commerce has decided to conduct a survey to estimate the proportion of adults between the ages of 25 and 35 living in the metropolitan area who have a college degree in a high-technology field. The chamber hopes to use the survey’s results to attract more high-technology firms to the region. The chamber wants the survey to estimate the population proportion within a margin of error of 0.03 percentage points with a level of confidence of 95%.
a. If the chamber has no information concerning the proportion of adults between the ages of 25 and 35 who have a college degree in a high-technology field before the survey is taken, how large a sample size must be used?
b. Suppose the chamber conducted a pilot study of 200 adults between the ages of 25 and 35 that indicated 28 with the desired attribute. How large a sample would be needed for the survey to estimate the population proportion within a margin of error of ± 0.03 with a 95% level of confidence?