The department of transportation wants to estimate the proportion of vehicles on Interstate 35 between the hours of midnight and 5:00 AM that are 18-wheel tractor trailers. Highway department officials counted vehicles at different locations on the interstate for several nights during this time period. Of the 3,481 vehicles counted, 927 were 18-wheelers. (adapted from [Black 2012])
Construct a 99% confidence interval for the proportion of vehicles on I-35 during this time period that are 18-wheelers.
How might this interval be useful to planners in the department of transportation?