A travel website would like to estimate the difference between the average renta
ID: 3368738 • Letter: A
Question
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. Complete parts a and b.
Sample mean
Sample size
Population standard deviation
Automatic
?$398.50398.50
5151
?$2121
Manual
?$328.90328.90
3636
?$2525
a. Construct a
9595?%
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
left parenthesis $ nothing comma $ nothing right parenthesis$,$.
?(Round to the nearest cent as? needed.)
Sample mean
Sample size
Population standard deviation
Automatic
?$398.50398.50
5151
?$2121
Manual
?$328.90328.90
3636
?$2525
Explanation / Answer
z value at 95% = 1.96
CI = ( x1 - x2) +/- z * sqrt(s1^2/n1 + s2^2/n2)
= (398.50 ,- 328.90) +/- 1.96 * sqrt(21 ^2/51+ 25^2/36))
= (59.6044 , 79.5956)
The 95% CI is (59.6044 , 79.5956)
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