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 5 years of the actual mean with a confidence level of 98%, 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 17 years.
Sample Size:
To determine the sample size required, we can use the formula for the sample size calculation:
n = (Z * σ / E) ^ 2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = standard deviation
E = margin of error
In this case, the desired confidence level is 98%, which corresponds to a Z-score of 2.33 (since the confidence level is divided equally between the two tails of the normal distribution). The margin of error, E, is 5.
n = (2.33 * 17 / 5) ^ 2
n = (40.61 / 5) ^ 2
n = 8.12 ^ 2
n = 66.01
Therefore, you should include at least 66 citizens in your sample to estimate the mean age of the citizens living in your community with a confidence level of 98% and a margin of error of 5 years.