Question

Estimate the minimum sample size needed to achieve the margin of error

E=0.023

for a​ 95% confidence interval.

Answer 1

Solution :

Given that,

= 0.50

1 - = 1 -0.50 = 0.50

margin of error = E = 0.023

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

Z_/2 = 1.960

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.960/0.023)² *0.50*0.50

= 1816

sample size = n = 1816