Question

solve the problem.

1. the following confidence interval is obtained for a population proportion, p: (0.688, 0.724). use these confidence interval limits to find the point estimate, $hat{p}$.

a) 0.708 b) 0.724 c) 0.706 d) 0.688

1. the following confidence interval is obtained for a population proportion, p: 0.724 < p < 0.752. use these confidence interval limits to find the margin of error, e.

a) 0.028 b) 0.014 c) 0.015 d) 0.738

Explanation:

Step1: Recall point - estimate formula

The point estimate $\hat{p}$ for a population proportion confidence interval $(a,b)$ is given by $\hat{p}=\frac{a + b}{2}$.
For the interval $(0.688,0.724)$, we have $a = 0.688$ and $b=0.724$.
So, $\hat{p}=\frac{0.688 + 0.724}{2}=\frac{1.412}{2}=0.706$.

Step2: Recall margin - of - error formula

The margin of error $E$ for a population proportion confidence interval $(a,b)$ is given by $E=\frac{b - a}{2}$.
For the interval $(0.724,0.752)$, we have $a = 0.724$ and $b = 0.752$.
So, $E=\frac{0.752-0.724}{2}=\frac{0.028}{2}=0.014$.

Answer:

1. C. 0.706
2. B. 0.014