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 be99​% confident that his estimate is in error by no more thanthree percentage points?

a) Assume that nothing is known about the percentage of computers with new operating systems.

n=

Answer 1

Solution :

Given,

E = 0.03

c = 99% = 0.99

When is not given then we used,

or p = 0.5

1 - 1- p = 1 - 0.5 = 0.5

Now,

= 1 - c = 1 - 0.99 = 0.01

/2 = 0.005

= 2.576 ....... (using z table)

The sample size for estimating the proportion is given by

n =

= (2.576)² * 0.5 * 0.5 / (0.03²)

= 1843.2711

= 1844 ..(round to the next whole number)

Answer : Required Sample size is n = 1844