Consider again the problem of estimating the mean age, , of all people in the civilian labor

Consider again the problem of estimating the mean age, μ, of all people in the civilian labor force. In Example 8.7 shown below, we found that a sample size of 2250 is required to have a margin of error of 0.5 year and a 95% confidence level. Suppose that, due to financial constraints, the largest sample size possible is 900. Determine the greatest confidence level, given that the margin of error is to be kept at 0.5 year. 

Example 8.7

Consider again the problem of estimating the mean age, μ, of all people in the civilian labor force. Determine the sample size needed in order to be 95% confident that μ is within 0.5 year of the point estimate. Find a 95% confidence interval for μ if a sample of the size determined in part (a) has a mean age of 43.8 years.