19. (10 points) A large rental car agency has a large fleet of cars. The company

Question

19. (10 points) A large rental car agency has a large fleet of cars. The company keeps careful records of the number of miles on the odometer for each car. They know that for all of the cars in their fleet this odometer mileage has an average of 22,300 miles with a standard deviation of 11,200 miles. The director of maintenance for the company ordered his assistant to randomly select 100 cars for detailed inspection. The sampled cars had an average mileage of 15,730. The director was concerned that the average mileage of these cars was lower than he expected. The assistant said this would just be the result of random sampling variability. Is the assistant correct that this is likely to have occurred by random sampling variability?

Explanation / Answer

Here the information about the population is given as below:

population mean = = 22300 & population std deviation = = 11200

Now the director has ordered his assistance to randomly select a sample of

n =100 with x = 15730

Now the director was concerned with low mileage and so he has to form hypothesis

Ho(null hypothesis):   = 22300

Ha(alternate hypothesis) : < 22300

So we have to calculate Z stat here

Z= (x-)/(/sqrt(n)) = (15730-22300)/(11200/sqrt(100)) = -5.866

Z= -5.866

Since this is a lower tail test as the < sign in alternate hypothesis talks about this

So we need to find the critical Z value for lower tail at 95% confidence level

which is Zcritical= -1.65 (In Z table check for value 0.05 & find coordinates of Z)

So here Z<Zcritical & so we have to reject Ho and so we can say that the avg is less than 22300

and so we can conclude that the assistance was wrong since such a large difference can't be due to random sampling.

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

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