Question

Find an estimate of the sample size needed to obtain a margin of error of

0.06

for the​ 95% confidence interval of a population​ mean, given a sample standard deviation of

0.8

Do not round until the final answer.

Answer 1

Solution

standard deviation = =s =0.8

Margin of error = E = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

n = ( 1.96* 0.8 / 0.06)2

n =682.95

Sample size = n =683 rounded