Question

Scores on a Statistics Final Exam are normally distributed. Using a​ 95% confidence​ level, find the sample size necessary to predict the population mean within 3 points. Assume the population standard deviation is 8 points.

Answer 1

Solution :

Given that,

standard deviation =s =  $\sigma$ =8

Margin of error = E = 3

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* 8 /3 )²

n =27

Sample size = n =27