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	​$417.50

55

​$24

Manual	​$365.60

33

​$28

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

left parenthesis $ nothing comma $ nothing right parenthesis

.

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

b. Based on the results from part​ a, can you conclude that a difference exists in the average rental price of the two types of​ cars?

Since the confidence interval

▼

does

does not

include​ $0, there is

▼

sufficient

insufficient

evidence to conclude that a difference exists in the average price of the two types of cars.

Answer 1

Ans:

Assumption:Population variances are not equal.

a)df=33-1=32

critical t value=tinv(0.1,32)=1.694

90% confidence interval for difference in means

=(417.50-365.60)+/-1.694*sqrt((24^2/55)+(28^2/33))

=51.9+/-9.91

=(41.99, 61.81)

b)

Since the confidence interval does not include​ $0, there is sufficient evidence to conclude that a difference exists in the average price of the two types of cars.