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A travel website would like to estimate the difference between the average rental price of a car with automatic transmission versus the average rental price of a car with manual transmission at a certain airport. The table below shows the average? one-week rental prices for two random? samples, as well as the population standard deviations and sample sizes for each type of car.

                               Sample mean                         Sample size                    Population standard deviation

Automatic                 $406.30                                       $52                                             ?$24

Manual                     $365.60                                       $38                                              $29

a. Construct a 90?% confidence interval to estimate the difference in the average cost of a? one-week rental between these two types of cars at the airport.

Let the cars with automatic transmissions be population 1 and the cars with manual transmissions be population 2.

The confidence interval is $ ,  $.

?(Round to the nearest cent as? needed.)

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