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 95% confident that his estimate is in error by no more than three percentage points question mark?
a. Assume that nothing is known about the percentage of computers with new operating systems. n=_.(Round up to the nearest integer.)
b. Assume that a recent survey suggests that about 96% of computers use a new operating system. n=_.(Round up to the nearest integer.)

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JeanaShupp JeanaShupp · Answer 1 · 2020-03-25T04:27:53+01:00

Answer: a. n= 1068

b. n= 164

Step-by-step explanation:

The formula to find the sample size :

[tex]n=p(1-p)(\dfrac{z^{*}}{E})^2[/tex]

, where p=prior population proportion , z* = critical z-value and E = Margin of error.

Here , let p=proportion of computers that use a new operating system.

Given : Confidence level = 95%

i.e. z* = 1.96 [by z-table]

Margin of error : E = 3% =0.03

a. If p is unknown , then we assume p=0.5

Then, [tex]n=(0.5)(1-0.5)(\dfrac{1.96}{0.03})^2=1067.11111\approx1068[/tex]

i.e. n= 1068

b. p=0.96

Then, [tex]n=(0.96)(1-0.96)(\dfrac{1.96}{0.03})^2=163.908266667\approx164[/tex]

i.e. n= 164.