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

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 87​% 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) only slightly increases 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) does not change the sample size.

Answer 1

Given that, margin of error (E) = 0.03 (3%)

A 90% confidence level has significance level of 0.10 and critical value is,

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

We want to find, the sample size (n),

=> n = 752

b) Assume that a recent survey suggests that about 87​% of computers use a new operating system. That is p = 0.87,

Therefore, required sample size (n) is,

=> n = 340

c) By part a) and b) we can say that, additional survey information reduces the sample size.

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