Question

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?

Short answer

The best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities is 0.720.

Step-by-step solution

Given information

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.

Compute the best point estimate

The best point estimate for the population proportion is the sample proportion.

The best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities is computed as follows:

$$\begin{gathered} \hat{\mathbf{p}}\mathbf{=}\frac{\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{f}\mathbf{i}\mathbf{d}\mathbf{e}\mathbf{n}\mathbf{c}\mathbf{e}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{l}\mathbf{i}\mathbf{m}\mathbf{i}\mathbf{t}\mathbf{+}\mathbf{u}\mathbf{p}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{f}\mathbf{i}\mathbf{d}\mathbf{e}\mathbf{n}\mathbf{c}\mathbf{e}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{l}\mathbf{i}\mathbf{m}\mathbf{i}\mathbf{t}}{\mathbf{2}} \\ =\frac{0.692+0.748}{2} \\ =0.720 \end{gathered}$$

Thus, the best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities is 0.720.