Question

We want to estimate the mean weekly earnings of students at a particular college with 95% confidence. How many students must be randomly selected so that the sample mean is within $1 of the population mean? Population standard deviation is known to be $10.

Answer 1

Solution :

Given that,

standard deviation =  $\sigma$ =10

Margin of error = E = 1

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* 10 /1 )²

n =384.16

Sample size = n =384