Question

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 97%, 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 19 years.

Sample Size:

Answer 1

Solution :

Given that,

Population standard deviation = =19

Margin of error = E = 4

At 97% confidence level

= 1-0.97% =1-0.97 =0.03

/2 =0.03/ 2= 0.015

Z/2 = Z_{0.015 = 2.17}

Z/2 = 12.17

sample size = n = [Z_/2* / E] ²

n = [ 2.17 * 19 /4 ]²

n = 106

Sample size = n = 106