Question
Express the confidence interval \( 0.444
Ask by Malone John. in the United States
Mar 20,2025
Ask by Malone John. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \hat{p} \pm E = 0.555 \pm 0.111 \)
Solution
1. Find the midpoint of the interval:
\[
\hat{p} = \frac{0.444 + 0.666}{2} = \frac{1.11}{2} = 0.555
\]
2. Calculate the margin of error:
\[
E = \frac{0.666 - 0.444}{2} = \frac{0.222}{2} = 0.111
\]
Thus, the confidence interval expressed in the form \( \hat{p} \pm E \) is:
\[
0.555 \pm 0.111
\]
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Simplify this solution Mind Expander
To express the confidence interval \( 0.444 < p < 0.666 \) in the form \( \hat{p} \pm E \), we first need to find the midpoint \( \hat{p} \) and the margin of error \( E \). 1. Calculate \( \hat{p} \) (the midpoint): \[ \hat{p} = \frac{0.444 + 0.666}{2} = \frac{1.110}{2} = 0.555 \] 2. Calculate \( E \) (the margin of error): \[ E = 0.666 - \hat{p} = 0.666 - 0.555 = 0.111 \] (You can also calculate \( E \) as \( \hat{p} - 0.444 = 0.555 - 0.444 = 0.111 \) for confirmation.) Thus, we can express the confidence interval as: \[ \hat{p} \pm E = 0.555 \pm 0.111 \]
