Question

Express the confidence interval (0.038,0.088) in the form of p−E

Answer 1

Given:

$confidence-interval:(0.038,0.088)$

To Determine:The expression of the given in the form

$\hat{p}-E

Solution

ˆp will be halfway between our lower- and upper-bound, and so we take the average of the two bounds

Let us find the average of the interval

[tex]p=\frac{0.038+0.088}{2}$$\begin{gathered} p=\frac{0.126}{2} \\ p=0.063 \end{gathered}$

Therefore, we have

$\begin{gathered} So \\ \hat{p}-E=0.038 \\ 0.063-E=0.038 \\ 0.063-0.038=E \\ 0.025=E \\ OR \end{gathered}$$\begin{gathered} \hat{p}+E=0.088 \\ 0.063+E=0.088 \\ E=0.088-0.063 \\ E=0.025 \end{gathered}$

Hence, we have

0.063 - 0.025 < p < 0.063 + 0.025