Chapter 7, Problem 1CQQ

Celebrities and the Law Here is a 95% confidence interval estimate of the proportion of adults who say that the law goes easy on celebrities: 0.692 < p < 0.748 (based on data from a Rasmussen Reports survey). What is the best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities?

To determine

To find: The best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities.

Answer to Problem 1CQQ

The point estimate of the proportion of adults in the population who say that the law goes easy on celebrities is 0.72.

Explanation of Solution

Given info:

The 95% confidence interval estimate of the proportion of adults who say that the law goes easy on celebrities is, $0.692<p<0.748$.

Calculation:

Point estimate $\left(\widehat{p}\right)$:

The formula for point estimate $\widehat{p}$ is,

$\widehat{p}=\frac{\left(\text{Upper confidence limit}\right)+\left(\text{Lower confidence limit}\right)}{2}$

Substitute 0.748 for upper confidence limit and 0.692 for lower confidence limit in the point estimate formula.

$\begin{array}{c}\widehat{p}=\frac{\text{0}\text{.748}+\text{0}\text{.692}}{2}\\ =\frac{1.44}{2}\\ =0.72\end{array}$

Thus, the best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities $\left(\widehat{p}\right)$ is 0.72.