When the level of confidence and sample size remain the same,a confidence interval for a population proportion p will be ______________ when is larger than when is smaller.
A)Wider
B)Narrower
C)Neither A nor B,they will be the same.

Question

When the level of confidence and sample size remain the same,a confidence interval for a population proportion p will be ______________ when  is larger than when  is smaller.
A)Wider 
B)Narrower 
C)Neither A nor B,they will be the same.

Quizplus · Accepted Answer

The margin of error, which is the distance between the point estimate and the upper or lower bound of the confidence interval, is directly proportional to the standard error of proportion, which is the square root of (p*(1-p)/n). As the sample proportion approaches 0 or 1 (meaning that p is smaller or larger), the standard error gets smaller, which results in a narrower confidence interval. Conversely, as the sample proportion approaches 0.5, the standard error gets larger, which results in a wider confidence interval. Therefore, when the population proportion is smaller (11eb06d7_55e5_06b9_8177_c97469918bf4_TB1736_11 is larger), the standard error is smaller, and the interval is narrower. When the population proportion is larger (11eb06d7_55e5_06ba_8177_bb624674b58a_TB1736_11 is smaller), the standard error is larger, and the interval is wider.

When the Level of Confidence and Sample Size Remain the Same,a