Chapter 9.2, Problem 54E

To determine

To check: Whether this confidence interval could be used to say that the proportion of U.S adults who are in favor of weight loss is different from 0.55.

Answer to Problem 54E

Yes, it could be concluded that proportion of U.S adults who are in favor of weight loss is different from 0.55.

Explanation of Solution

Given:

Margin of error ( E ) = ±3% = 0.03

Point estimate $\left(\widehat{p}\right)=59\%=0.59$

Formula used:

The formula to compute the confidence interval is:

  $\begin{array}{c}\text{Confidence interval}=\text{ Point estimate}\pm \text{Margin of error}\\ =\widehat{p}\pm E\end{array}$

Calculation:

The confidence interval is computed as follows:

  $\begin{array}{c}\text{Confidence interval}=\widehat{p}\pm E\\ =0.59\pm 0.03\\ =\left(0.56,0.62\right)\end{array}$

Thus, the required confidence interval is $\left(0.56,0.62\right)$

Conclusion:

Since, 0.55 does not lie in the above computed confidence interval. Thus, it can be concluded that the proportion of U.S adults who are in favor of weight loss is different from 0.55.