A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon. You believe the claim is incorrect and find that a random sample of five cars has a mean gas mileage of 19 miles per gallon and a standard deviation of 4 miles per gallon. Assume the gas mileage of all of the company’s luxury sedans is normally distributed. At á = 0.05, test the company’s claim.

Question

A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon.  You believe the claim is incorrect and find that a random sample of five cars has a mean gas mileage of 19 miles per gallon and a standard deviation of 4 miles per gallon.  Assume the gas mileage of all of the company’s luxury sedans is normally distributed.  At á = 0.05, test the company’s claim.
•	What is the difference between a critical value and a test statistic?  
•	Decide whether you should use a normal sampling distribution or a t-sampling distribution to perform the hypothesis test.  
•	Why would you use a z-test rather than a t-test?  
•	Which do you think you will use more often?  Justify your decisions.  
•	Then use the distribution to test the claim.  
•	Write a short paragraph about the results of the test and what you can conclude about the claim.

Anonymous · Answer

Ho: Mean >= 21 (claim) Ha: mean < 21 t = 1.118 P-value = 0.163 Fail to reject Ho