Question

Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is $(0.09,0.26)$.

What is the margin of error?

Step 1 ：Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is \((0.09,0.26)\).

Step 2 ：The margin of error for a confidence interval is calculated as half the difference between the upper and lower bounds of the interval. In this case, the upper bound is 0.26 and the lower bound is 0.09.

Step 3 ：So, the margin of error would be \((0.26 - 0.09) / 2\).

Step 4 ：Calculating the above expression, we get the margin of error as 0.085.

Step 5 ：Final Answer: The margin of error is \(\boxed{0.085}\).