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 95​% confident that his estimate is in error by no more than five percentage points question marks?

Complete parts​ (a) through​ (c) below. Round to nearest integer.

Assume that nothing is known about the percentage of computers with new operating systems.

n= ?

Assume that a recent survey suggests that about 89​% of computers use a new operating system.

n = ?

Does the additional survey information from part​ (b) have much of an effect on the sample size that is​ required?

A - Yes, using the additional survey information from part​ (b) dramatically increases the sample size

B. - ​No, using the additional survey information from part​ (b) does not change the sample size.

C. - Yes, using the additional survey information from part​ (b) dramatically reduces the sample size.

D. - No, using the additional survey information from part​ (b) only slightly increases the sample size

Answer 1

Answer :

Given that :

Confidence interval = 95%

Accurate percentage E = 5% = 0.05

a)Assume that nothing is known about the percentage of computers with new operating systems :n

Here the percentage of proportion is not given so assume that p = 0.5

q = 1 - p = 1 - 0.5 = 0.5

Z at value 95% = 1.96

Here we need to find the sample size n :

therefore,

Sample size n = 384

b)Assume that a recent survey suggests that about 89​% of computers use a new operating system :

Here Confidence interval is given = 89%

p = 89% = 0.89

q = 1 - 0.89 = 0.11
So , Z value at 89% = 1.6

So,

therefore,

Sample size n = 100

c)Option C is correct.

Yes, using the additional survey information from part​ (b) dramatically reduces the sample size.

Because in part (a) sample size n = 384

And in part (b) sample size n = 100