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

99​%

confident that his estimate is in error by no more than

two

percentage

points?

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

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

n=nothing

​(Round up to the nearest​ integer.)

​b) Assume that a recent survey suggests that about

98​%

of computers use a new operating system.

n=nothing

​(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.

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

B.

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

C.

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

D.

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

Answer 1

Solution :

margin of error = E = 0.02

Z_/2 = 2.576

(a)

= 0.5

1 - = 0.5

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (2.576 / 0.02)² * 0.5 * 0.5

= 4148

sample size = n = 4148

(b)

= 0.98

1 - = 0.02

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (2.576 / 0.02)² * 0.98 * 0.02

= 326

sample size = n = 326

(c)

B.

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