It is known that the population variance equals 529. With a .95 probability, the sample size that needs to be taken if the desired margin of error is 4 or less is
A) 508.
B) 127.
C) 509.
D) 128.

Question

Quizplus · Accepted Answer

The formula for determining the sample size needed to find a desired margin of error is as follows:

n = (z^2 * σ^2) / E^2

Where:
n = sample size
z = z-score for desired level of confidence (in this case, .95 corresponds to a z-score of 1.96)
σ^2 = population variance (given as 529)
E = desired margin of error (given as 4)

Plugging in the values, we get:

n = (1.96^2 * 529) / 4^2
n = 128.15

Rounding up to the nearest integer, we get a required sample size of 128. Therefore, the answer is D.

It Is Known That the Population Variance Equals 529