Question

express the confidence interval (0.064, 0.154) in the form of \\( \hat { p } - e < p < \hat { p } + e \\).

\\( \square < p < \square \\) (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. Use the formula $\hat{p}=\frac{\text{lower limit}+\text{upper limit}}{2}$.
$$\hat{p}=\frac{0.064 + 0.154}{2}=\frac{0.218}{2}=0.109$$

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. Use the formula $E=\frac{\text{upper limit}-\text{lower limit}}{2}$.
$$E=\frac{0.154 - 0.064}{2}=\frac{0.09}{2}=0.045$$

Answer:

$0.109-0.045 < p < 0.109 + 0.045$, so $0.064 < p < 0.154$