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.

Automatic: Sample mean = $397.30 , Sample Size = 50, Pop. Standard Deviation = $20

Manual: Sample mean = $353.70, Sample Size = 32, Pop. Standard Deviation = $24

a. Construct a 95% 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 ( __, __).

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?

Answer 1

a) From standard normal tables, we have:

P( -1.96 < Z < 1.96 ) = 0.95

The standard error here is first computed here as:

Therefore, now the confidence interval here is obtained as:

This is the required 95% confidence interval for the difference between the 2 means

b) As the confidence interval above does not contain 0, therefore we can conclude that there exist a difference in the average rental price of the two type of cars.