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 one percentage point question mark Complete parts​ (a) through​ (c) below. ​a) Assume that nothing is known about the percentage of computers with new operating systems. n= ?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 1% = 0.01

At 90% confidence level the z is,

= 1 - 90%

= 1 - 0.90 = 0.10

/2 = 0.05

Z_/2 = Z _0.05 = 1.645

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

= ( 1.645 / 0.01)² * 0.5 * 0.5

= 6765.06

sample size = n = 6766