Q.52 - The Practice of Statistics for AP

Question

I collect an SRS of size n from a population and compute a $95\%$ confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

(a) Use a larger confidence level.

(b) Use a smaller confidence level. 

(c) Increase the sample size. 

(d) Use the same confidence level, but compute the interval n times. Approximately$5\%$ of these intervals will be larger. 

(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is $0.05$. 

Step-by-Step Solution

Answer

Correct answer is (a) Use a larger confidence level

Step 1: Given information

Given in the question that, I collect an SRS of size $n$ from a population and compute a $95\%$ confidence interval for the population proportion .

Step 2: Explanation

(a) A larger confidence level leads to better accuracy and thus the confidence interval will becomes wider.

(b) A smaller confidence level will decrease the accuracy and thus lessen the width of the confidence interval.

(c) Increasing the sample size increases the accuracy and thus the width of the confidence interval decreases.

(d) This method does not lead to ONE larger confidence interval.

(e) Incorrect, because (a) is a valid method to obtain a larger interval.