Question

USA Today (October 14,2002 ) reported that \(36 \%\) of adult drivers admit that they often or sometimes talk on a cell phone when driving. This estimate was based on data from a representative sample of 1,004 adult drivers. A margin of error of \(3.1 \%\) was also reported. Is this margin of error correct? Explain.

Short answer

To find out if the 3.1% margin of error quoted in the exercise is correct, we need to use the formula for the margin of error and compare the result to the value provided. It's essential to show how to apply the margin of error formula meticulously.

Step-by-step solution

Define the Variables

Firstly, we identify the variables from the problem. The sample proportion \(p\) is 0.36 (36%). The sample size \(n\), equals 1,004.

Apply Margin of Error Formula

We apply the margin of error formula \(E = Z \sqrt{\frac{{p(1-p)}}{n}}\). Here, we use the standard \(Z\) value of 1.96 for a 95% confidence interval, \(p=0.36\), and \(n=1004\). Then calculate the value.

Compare Calculated Margin of Error with Given Margin of Error

After calculating the margin of error, we compare it with the given margin of error of 3.1%. If they are close or approximately equal, the stated margin of error would be assumed correct. Otherwise, it isn't correct.