A researcher has estimated that she needs a sample of size n=100 from a population consisting of 1,000 elements.Recognizing that the sample represents 10% of the population,she decides to apply the finite population correction factor to her initial estimate.What is the corrected sample size?
A)10
B)84
C)105
D)91
E)95

Question

Quizplus · Accepted Answer

The finite population correction factor is applied when the sample size is more than 5% of the population size. In this case, since the sample represents 10% of the population, the correction factor should be used.

The corrected sample size can be calculated using the formula:
Corrected sample size = (Sample size)/(1 + (Population size - 1)/(Sample size))

Substituting the given values:
Sample size = 100
Population size = 1000

Corrected sample size = (100)/(1 + (1000 - 1)/(100))
= 91.07

Rounding off to the nearest whole number gives the corrected sample size as 91. Therefore, the correct choice is D).

A Researcher Has Estimated That She Needs a Sample of Size