Question

A manager wishes to estimate a population mean using a 90% confidence interval estimate that has a margin of error of +- 47.0. If the population standard deviation is thought to be 640, what is the required sample

size?

The sample size must be at least _?

Answer 1

Solution:

Given:

Confidence level = c = 90% = 0.90

Margin of Error = E = 47.0

Population standard deviation =

We have to find the required sample size n.

Formula:

Where Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

Thus the required sample size n = 502