express the confidence interval (0.023,0.091) in the form of $hat{p}-e

Question

express the confidence interval (0.023,0.091) in the form of $hat{p}-e < p < hat{p}+e$.

< (type integers or decimals.)

Accepted Answer

# Explanation:
## Step1: Calculate $\hat{p}$
$\hat{p}=\frac{0.023 + 0.091}{2}=\frac{0.114}{2}=0.057$
## Step2: Calculate $E$
$E=\hat{p}-0.023 = 0.057- 0.023=0.034$
# Answer:
$0.057 - 0.034<p<0.057 + 0.034$ or $0.023<p<0.091$ (the original form is also correct as we derived from it, but if we want in the new - derived form) $0.023<p<0.091$ can be rewritten as $0.057-0.034 < p<0.057 + 0.034$ where the left - hand side is $0.023$ and the right - hand side is $0.091$. So the answer is $0.023<p<0.091$ or more explicitly written as $0.057 - 0.034<p<0.057+0.034$ with $\hat{p}=0.057$ and $E = 0.034$. In the requested form: $0.023<p<0.091$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate $\hat{p}$

Step2: Calculate $E$

Answer: