Question

express the confidence interval (0.057,0.149) in the form of \\( \hat { p } - e < p < \hat { p } + e \\).

<p< (type integers or decimals.)

Explanation:

Step1: Calculate the point estimate ($\hat{p}$)

The point estimate $\hat{p}$ is the mid - point of the confidence interval.
$$\hat{p}=\frac{0.057 + 0.149}{2}=\frac{0.206}{2}=0.103$$

Step2: Calculate the margin of error ($E$)

The margin of error $E$ is the distance from the point estimate to either end of the confidence interval.
$$E=\hat{p}-0.057=0.103 - 0.057 = 0.046$$

Answer:

$0.103-0.046 < p < 0.103 + 0.046$