Question

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

E=0.206

for a​ 95% confidence interval.

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.206

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

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

= (1.96 / 0.206)² * 0.5 * 0.5

= 22.63

sample size = n = 23