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 3 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 24 years.

Answer 1

Solution

standard deviation =   =24

Margin of error = E = 3

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z/2 = Z0.015 = 2.17

sample size = n = [Z/2* / E] 2

n = ( 2.17*24 / 3 )2

n =301.3696

Sample size = n =301 rounded