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 90​% confident that his estimate is in error by no more than two percentage points question mark Complete parts​ (a) through​ (c) below.

​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 95​% 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

a.
given data,
margin of error =0.02
sample proportion =0.5
sample size is needed
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Sample Proportion = 0.5
ME = 0.02
n = ( 1.645 / 0.02 )^2 * 0.5*0.5
= 1691.266 ~ 1692      
  
b.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.5
ME = 0.02
n = ( 1.96 / 0.02 )^2 * 0.5*0.5
= 2401 ~ 2401          
c.
yes,
confidence interval changes the sample size also.