Testing gas mileage claims | Numerical analysis homework help

Testing Gas Mileage Claims

 Assume that you are working for the Consumer Protection Agency and have recently been getting complaints about the highway gas mileage of the new Dodge Caravans. Chrysler Corporation agrees to allow you to randomly select 40 of its new Dodge Caravans to test the highway mileage. Chrysler claims that the Caravans get 28 mpg on the highway. Your results show a mean of 26.7 and a standard deviation of 4.2. You support Chrysler’s claim.

1. Show why you support Chrysler’s claim by listing the P -value from your output. After more complaints, you decide to test the variability of the miles per gallon on the highway. From further questioning of Chrysler’s quality control engineers, you find they are claiming a standard deviation of 2.1.
2. Test the claim about the standard deviation.
3. Write a short summary of your results and any necessary action that Chrysler must take to remedy customer complaints.
4. State your position about the necessity to perform tests of variability along with tests of the means.

Section 8–5Testing Gas Mileage Claims

1. The hypotheses are H 0: m  28and H 1: m  28.Thevalue of our test statistic is t  1.96,and the associated P -valueis0.0287.We would reject Chrysler’s claim that the Dodge Caravans are getting 28mpg.
2. The hypotheses are H 0: s  2.1 and H 1: s  2.1. The value of our test statistic is and the associated P -value is approximately zero. We would reject Chrysler’s claim that the standard deviation is 2.1 mpg.