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 three percentage points question marks?

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

n=___

​b) Assume that a recent survey suggests that about 85​% of computers use a new operating system.

n=____

c) Does the additional survey information from part​ (b) have much of an effect on the sample size that is​ required?

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.03

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

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

= (2.576 / 0.03)2 * 0.5 * 0.5

= 1843.27

sample size = n = 1844

b) = 0.85

1 - = 1 - 0.85 = 0.15

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

= (2.576 / 0.03)2 * 0.85 * 0.15

= 940.06

sample size = n = 941

c) Yes, using the additional survey information from part (b) dramatically reduces the sample size.