Question

A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 95​% confident that his estimate is in error by no more than five percentage points?

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.05)² * 0.5 * 0.5

= 384.16

sample size = 385

385 computers must be surveyed in order to be 95​% confident that his estimate is in error by no more than five percentage points.