Study results indicate that the mean length of time people spend on a bus in a city is between 22.4 minutes and 26.5 minutes.
What is the study's margin of error?
\((22.4, 26.5)\)is caalled a confidence interval. The way you form a confidence interval is by adding and subtracting the margin of error from the sample mean. so
\(26.5=sample\ mean+margin\ of\ error\), and
\(22.4=sample\ mean-margin\ of\ error\).
Solve the system of equations by adding the two equations to eliminate margin of error and get
\(2\times sample\ mean=22.4+26.5=48.9\), or
So \(margin\ of\ error=26.5-24.45=2.05\).