Question

Loose ChangeUSA Todayreported that 40% of people surveyed planned to use accumulatedloose 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:

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

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