Question

Assume that you want to construct a​ 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the​ 95% confidence interval. The sample standard deviation is given below. Margin of error =​$5​,standard deviation=​$25

The required sample size is ?????

​(Round up to the nearest whole number as​ needed.)

Answer 1

Solution :

Given that,

$\sigma$ = $25

E = $5

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96

sample size n = ( Z_$\alpha$/2* $\sigma$ / E )²

n = ( 1.96 * 25 / 5)²

^{n =96.04}

^{n= 96}