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 wider nor narrower (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 wider nor narrower (they will be the same)

Quizplus · Accepted Answer

The margin of error of a confidence interval for a population proportion is directly proportional to the square root of (p(1-p)/n), where p is the sample proportion and n is the sample size. If the sample size remains the same but the population proportion increases (i.e. p is larger), the margin of error will also increase, resulting in a wider confidence interval. Conversely, if the population proportion decreases (i.e. p is smaller), the margin of error will decrease, resulting in a narrower confidence interval. Therefore, the answer is A.

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