express the confidence interval (0.017,0.093) in the form of $ \hat { p } - e

Question

express the confidence interval (0.017,0.093) in the form of $ \hat { p } - e < p < \hat { p } + e $.
$ \square < p < \square $ (type integers or decimals.)

Accepted Answer

# Explanation:
## Step1: Calculate $\hat{p}$
$\hat{p}=\frac{\text{lower limit}+\text{upper limit}}{2}=\frac{0.017 + 0.093}{2}=\frac{0.11}{2}=0.055$
## Step2: Calculate $E$
$E=\frac{\text{upper limit}-\text{lower limit}}{2}=\frac{0.093-0.017}{2}=\frac{0.076}{2}=0.038$

# Answer:
$0.055 - 0.038<p<0.055 + 0.038$
So, $0.017<p<0.093$ (Note: This is just re - stating the original interval in the required form. The values of $\hat{p}=0.055$ and $E = 0.038$ are calculated as above, but when we substitute into $\hat{p}-E<p<\hat{p}+E$, we get back the original interval values. The left - hand side is $0.055-0.038 = 0.017$ and the right - hand side is $0.055+0.038=0.093$)

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate \(\hat{p}\)

Step2: Calculate \(E\)

Answer: