You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 95%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 25 years.

The number of citizens that should be included in the sample is 151.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean is:

The margin of error for this interval is:

The information provided is:

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

*Use a z-table.

Compute the sample size required as follows:

Thus, the number of citizens that should be included in the sample is 151.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.