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

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 stem. 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? Complete parts (a) through (c) below. 19. 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. (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? O A. No, using the additional survey information from part (b) only slightly increases the sample size. O B. Yes, using the additional survey information from part (b) dramatically increases the sample size O C. No, using the additional survey information from part (b) does not change the sample size. D. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

Explanation / Answer

Solution:- Given that information 90% confidence interval Z = 1.645 , E = 0.03

Formula : n = p*q*(Z/E)^2

a) p = 0.5

n = 0.5*0.5*(1.645/0.03)^2

n = 751.6736

n = 752

b)p = 0.87 , q = 0.13

n = 0.87*0.13*(1.645/0.03)^2

n = 340.0571

n = 340

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

The required sample size decreases dramatically from 752 to 340, with the addition of the survey information.

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