Problem

Suppose that the confidence interval $(0.56,0.76)$ is given for a population proportion, $p$. Use these confidence interval limits to find the point estimate, $\widehat{p}$, and the margin of error, $E$.

Solution

Step 1 :Given the confidence interval for a population proportion, \(p\), is \((0.56,0.76)\).

Step 2 :The point estimate, \(\widehat{p}\), is the midpoint of the confidence interval. It can be calculated as the average of the lower and upper limits of the confidence interval.

Step 3 :Calculate the point estimate, \(\widehat{p}\), as \((0.56 + 0.76) / 2 = 0.66\).

Step 4 :The margin of error, \(E\), is the difference between the point estimate and either the lower or upper limit of the confidence interval.

Step 5 :Calculate the margin of error, \(E\), as \(0.66 - 0.56 = 0.10\).

Step 6 :Final Answer: The point estimate, \(\widehat{p}\), is \(\boxed{0.66}\) and the margin of error, \(E\), is approximately \(\boxed{0.10}\).

From Solvely APP
Source: https://solvelyapp.com/problems/12875/

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