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.

automatic manual

sample mean $414.60 376.20

sample size 46 38

population std dev $22 $27

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. ($ ,$ ) round to the nearest cent.

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)

Critical value:

Z/2 = Z 0.05/2 = 1.96              ...................Using standard Normal table

95% Confidnece interval:

b) Here, 0 is Not included in above confidence interval.

So, We Reject Ho at 5% Level of significance.

We can conclude that a difference exists in the average rental price of the two types of​ cars