Use the given confidence interval to find the margin of error and the sample proportion.
\[
(0.767,0.791)
\]
$E=\square$ (Typeran integer or a decimal.)
$\hat{p}=\square$ (Type an integer or a decimal.)
Answer
Final Answer: The margin of error (E) is \(\boxed{0.012}\) and the sample proportion (\(\hat{p}\)) is \(\boxed{0.779}\)
Step 1 ：Given the confidence interval \((0.767,0.791)\)
Step 2 ：The margin of error (E) in a confidence interval is calculated as half the width of the confidence interval. So, we calculate E as \(E = \frac{0.791 - 0.767}{2} = 0.012\)
Step 3 ：The sample proportion (\(\hat{p}\)) is the midpoint of the confidence interval. So, we calculate \(\hat{p}\) as \(\hat{p} = \frac{0.791 + 0.767}{2} = 0.779\)
Step 4 ：Final Answer: The margin of error (E) is \(\boxed{0.012}\) and the sample proportion (\(\hat{p}\)) is \(\boxed{0.779}\)
