Question

interested in estimating the mean age of the citizens living in your community in order to do this your plan on constructing a confidence interval however you are not show how many citizens should be included in the sample if you want your sample estimate to be within 4 years of the actual name with a confidence level of 96% how many citizens should be included in your sample as long that the standard deviation of the ages of all the citizen in the community 25 years

Answer 1

Solution :

Given that,

Population standard deviation = = 25

Margin of error = E = 4

At 96% confidence level the z is,

= 1 - 96%

= 1 - 0.96 = 0.04

/2 = 0.02

Z/2 = Z0.02 = 2.054

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

n = [2.054 * 25 / 4]2

n = 164.80

Sample size = n = 165