4. You plan to develop a new software system that you believe will surpass the s

Question

4. You plan to develop a new software system that you believe will surpass the success of Google and Facebook combined. In planning for the operating system that you will use, you need to estimate the percentage of computers that use Windows. How many computers must be surveyed in order to be 99% confident that your estimate is in error by no more than one percentage point?

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

b. Assume that a recent survey suggest that about 90% of computers use Windows operating systems (based on data from Net Applications).

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

Explanation / Answer

Sample Size Problem:

n = (zc / E)^2*p*q

Question a)

For 99% confidence we get the critical zc value as 2.58

p = 0.5

q = 1 – p = 1- 0.5 = 0.5

E = 0.01

n = (2.58/0.01)^2*0.5*0.5

   = 16641

Answer: 16641

Question b)

For 99% confidence we get the critical zc value as 2.58

p = 0.9

q = 1 – p = 1- 0.9 = 0.1

E = 0.01

n = (2.58/0.01)^2*0.9*0.1

   = 5990.8

Answer: 5991

Question c)

Answer: Yes, the additional survey information from part ( b ) have much of an effect on the sample size that is required. The sample size got decreased in part ( b ).

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