In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.5 mpg and approximately normally distributed. A consumer group conducts its own tests on a simple random sample of 12 cars of this model and finds that the mean gas mileage for their vehicles is 31.6 mpg with a standard deviation of 3.4 mpg. a. Perform a test to determine if these data support the contention that the true mean gas mileage of this model of car is different from the published value. b. Perform a test to determine if these data support the contention that the true mean gas mileage of this model of car is less than the published value. c. Explain why the answers to part a and part b are different.