Question: Bastien, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 6 miles per gallon.

a. With a 0.05 level of significance, do a right-sided test for the population mean of 50 to see if the claim is legitimate.

b. What is the p-value associated with the sample results?