Chapter 12, Problem AP4.4CPT

To determine

To find out which of the following is the margin of error for this confidence interval.

Answer to Problem AP4.4CPT

Option (a) is the correct option.

Explanation of Solution

Remember that the confidence interval for proportion takes the form to the left, we'll be using this to solve for margin of error.If we take the second value and subtract the first value, we will get the form to the left.As we can see here, to solve for margin of error, we will take the second value of the confidence interval, subtract the first value, then divide by two. Thus, we have,

  $\begin{array}{l}(\widehat{p}-MOE,\widehat{p}+MOE)\\ \Rightarrow (\widehat{p}+MOE)-(\widehat{p}-MOE)=2\times MOE\\ \Rightarrow MOE=\frac{0.257-0.183}{2}\\ =0.037\end{array}$

Thus, the option (a) is the correct option.