A travel website would like to estimate the difference betweenthe average rental price of a car with automatic transmissionversus the average rental price of a car with manual transmissionat a certain airport. The table below shows the average​ one-weekrental prices for two random​ samples, as well as the populationstandard deviations and sample sizes for each type of car. Completeparts a and b.
| Sample mean | Sample size | Population standard deviation |
|---|
Automatic | ​$411.90 | 54 | ​$23 |
|---|
Manual | ​$355.90 | 34 | ​$27 |
|---|
a. Construct a
9595​%
confidence interval to estimate the difference in the averagecost of a​ one-week rental between these two types of cars at theairport.
Let the cars with automatic transmissions be population 1 andthe cars with manual transmissions be population 2.
The confidence interval is
left parenthesis $ nothing comma $ nothing rightparenthesis$,$.
​(Round to the nearest cent as​ needed.)
