Question

A programmer plans to develop a new software system. In planning for the operating system that...

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?

Complete parts​ (a) through​ (c) below.

​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.)

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

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

B.Yes, using the additional survey information from part​ (b) dramatically increases 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.

Homework Answers

Answer #1

a)\

here margin of error E = 0.030
for95% CI crtiical Z          = 1.960
estimated proportion=p= 0.500
required sample size n =         p*(1-p)*(z/E)2= 1068.00

b)

here margin of error E = 0.030
for95% CI crtiical Z          = 1.960
estimated proportion=p= 0.960
required sample size n =         p*(1-p)*(z/E)2= 164.00

c)

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

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