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 two percentage points? a)Assume that nothing is known about the percentage of computers with new operating systems.
2 answers:
Answer: 2401
Step-by-step explanation:
Formula to find the sample size is given by :-
, where p = prior population proportion.
= Two -tailed z-value for
E= Margin of error.
As per given , we have
Confidence level :
⇒
Two -tailed z-value for
E= 2%=0.02
We assume that nothing is known about the percentage of computers with new operating systems.
Let us take p=0.5 [we take p= 0.5 if prior estimate of proportion is unknown.]
Required sample size will be :-
Hence, the number of computer must be surveyed = 2401
<em>Answer: </em>
<em>n = 1067</em>
<em>Step-by-step explanation: </em>
<em />
<em>Since nothing is known, we would assume that 50% of the computers use the new operating system.
</em>
<em>So, standard error = 0.5/SQRT(n)
</em>
<em>Z-value for a 95% CI = 1.9596
</em>
<em>So, margin of error = 1.9596 x 0.5 / SQRT(n) = 0.03
</em>
<em>So, n = 1067 (approx.)</em>
<em />
<em>This will be your approximate answer : n = 1067 </em>
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