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
99​% confident that his estimate is in error by no more than two percentage points question marks?
B) Assume that a recent survey suggests that about 89​% of computers use a new operating system.

Answer 1

Solution :

Given that,

= 89% = 0.89

1 - = 1 - 0.89 = 0.11

margin of error = E = 2% = 0.02

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = Z _0.005 = 2.576

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

= ( 2.576 / 0.02 )² * 0.89 * 0.11

= 1624.10

sample size = n = 1625