Chapter 9.2, Problem 56E

To determine

To find: Whether there are sufficient evidence to conclude that the proportion of U.S adults who are saying that they are interesting in losing the weight is different from 0.55.

Answer to Problem 56E

Yes, there are sufficient evidences.

Explanation of Solution

Given:

Sample proportion $\left(\widehat{p}\right)=59\%=0.59$

Margin of error $\left(E\right)=\pm 3\%=\pm 0.03$

Concept used:

The formula to compute the confidence interval for population proportion is:

  $\text{Confidence interval}=\widehat{p}\pm E$

Calculation:

The 95% confidence interval could be calculated as:

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

Thus, the confidence interval is (0.56, 0.62)

Conclusion:

Since, 0.55 does not lie in the above computed confidence interval. Thus, there are sufficient evidence to conclude that the proportion of U.S adults who are saying that they are interesting in losing the weight is different from 0.55.