Question

express the confidence interval (0.077, 0.141) in the form of \\( \hat { p } - e < p < \hat { p } + e \\).
\\( < p < \\) (type integers or decimals.)

Explanation:

Step1: Find the mid - point ($\hat{p}$)

The mid - point of the interval $(a,b)$ is given by $\hat{p}=\frac{a + b}{2}$. Here $a = 0.077$ and $b=0.141$.
$$\hat{p}=\frac{0.077+0.141}{2}=\frac{0.218}{2}=0.109$$

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

The margin of error $E$ is given by $E=\frac{b - a}{2}$.
$$E=\frac{0.141 - 0.077}{2}=\frac{0.064}{2}=0.032$$

Answer:

$0.109-0.032 < p<0.109 + 0.032$