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