Question

Loose Change USA Todayreported that 40% of people surveyed planned to use accumulated loose change for paying bills. The margin of error was given as $\pm$3.1 percentage points. Identify the confidence interval that corresponds to that information.

Short answer

The confidence interval that corresponds to the provided information is 36.9% < p < 43.1%.

Step-by-step solution

Given information

The percentage of people who planned to use accumulated loose change for paying bills is 40%.

The margin of error is $\pm 3.1$percentage points.

Compute the confidence interval

From the given information, the following points can be concluded:

The proportion of people who planned to use accumulated loose change for paying bills is $\hat{p}=0.40$.

The margin of error is $E=0.031$.

The confidence interval is computed as follows:

$$\begin{gathered} \left(\hat{p}-E,\hat{p}+E\right)=\left(0.40-0.031,0.40+0.031\right) \\ =\left(0.369,0.431\right) \end{gathered}$$

Therefore, the confidence interval is36.9% < p < 43.1%.