When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that is estimated to be, the sample size required __________.
A)is smaller
B)is larger
C)is not affected
D)can be smaller, larger or unaffected

Question

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that  is estimated to be, the sample size required __________.
A)is smaller 
B)is larger 
C)is not affected 
D)can be smaller, larger or unaffected

Quizplus · Accepted Answer

The sample size required increases as the estimated proportion gets closer to 0 or 1, so the closer to 0.50 the estimated proportion is, the larger the sample size required. As the estimated proportion moves closer to 0.50, the variability of the sample increases, which means a larger sample size is required to achieve the same level of precision and confidence. This is because the standard error of the sample mean depends on the proportion, and when the proportion is closer to 0.50, the standard error is larger. Therefore, option B is the best choice.

When Determining the Sample Size for a Proportion for a Given