Question

A company has found that its staff is idle 40 percent of the time. However, they would like to make sure that they have observed the process enough to rely on their previous findings to within 3 with a confidence of 99 percent.

The z-value for the confidence of 99% is 2.58.

Answer 1

Solution,

Given that,

= 0.40

1 - = 1 - 0.40 = 0.60

margin of error = E = 0.03

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z_/2 = Z_0.005 = 2.58  

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.58 / 0.03)² * 0.40 * 0.60

= 1775.04

sample size = n = 1776