Question

A manager wishes to estimate a population mean using a 99​% confidence interval estimate that has a margin of error of plus or minus±48.0 If the population standard deviation is thought to be 630​, what is the required sample​ size?

The sample size must be at least?

Answer 1

Solution :

Given that,

Population standard deviation = = 630

Margin of error = E = 48

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z_/2* / E) ²

n = (2.576 * 630 / 48)²

n = 1143.1

n = 1144

The sample size must be at least 1144