Question

A programmer plans to develop a new software system. In planning for the operating system he will use, he needs to estimate the percentage of computers that use a new operating systems. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than four percentage points?A) Assume that nothing is known about the percentage of computers with new operating systems. n = ?B) Assume that a recent survey suggests that 99% of computers use a new operating system. n = ?

Answer 1

Answer: a) 423  b) 17

Step-by-step explanation:

As per given , we have

E=4% = 0.04

Confidence level : 90%

The critical value for 90% confidence interval : z*=1.645

a) When the prior estimate of the population proportion is unknown , then the formula to find the sample size is given by :-

$n=0.25(\dfrac{z^*}{E})^2$

, where E = margin of error.

z* = Critical value.

Required sample size : $n=0.25(\dfrac{1.645}{0.04})^2$  (Substitute the given values in the formula)

$n=0.25(41.125)^2$

$n=0.25(41.125)^2=422.81640625\approx423$

i.e. n= 423

b) When the prior estimate of the population proportion is known , then the formula to find the sample size is given by :-

$n=p(1-p)(\dfrac{z^*}{E})^2$

, where p = Population proportion from prior study.

E = margin of error.

z* = Critical value.

here p= 0.99

$n=0.99(1-0.99)(\dfrac{1.645}{0.04})^2$      (Substitute the given values in the formula)

$n=0.0099(41.125)^2=16.7435296875\approx17$

i.e. n= 17