Problem

Express the confidence interval $(0.015,0.089)$ in the form of $\hat{p}-E< p< \hat{p}+E$.

Answer

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Answer

\(\boxed{0.015 < p < 0.089}\) is the final answer.

Steps

Step 1 :The confidence interval is given as (0.015, 0.089).

Step 2 :This can be expressed in the form \(\hat{p}-E

Step 3 :The point estimate \(\hat{p}\) is the midpoint of the interval and the margin of error E is the distance from the point estimate to either end of the interval.

Step 4 :Calculate the point estimate \(\hat{p}\) as the midpoint of the interval: \(\hat{p} = \frac{0.015 + 0.089}{2} = 0.052\).

Step 5 :Calculate the margin of error E as the distance from the point estimate to either end of the interval: \(E = \hat{p} - 0.015 = 0.037\).

Step 6 :Substitute \(\hat{p}\) and E into the inequality: \(0.052 - 0.037 < p < 0.052 + 0.037\).

Step 7 :\(\boxed{0.015 < p < 0.089}\) is the final answer.

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