Question

The population standard deviation for the employee turnover of each department in a company is 3.7 employees. If we want to be 95% confident that the sample mean is within 1 employee of the true population mean, what is the minimum sample size that can be taken?

z 0.10	z 0.05	z 0.025	z 0.01	z 0.005
1.282	1.645	1.960	2.326	2.576

Use the table above for the z-score, and be sure to round up to the nearest integer.

Provide your answer below:

Answer 1

:

Solution

standard deviation =s =   =3.7

Margin of error = E = 1

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 3.7 / 1 )2

n =52.59

Sample size = n =53