Bastien, Inc has been manufacturing small automobiles that have averaged 50 miles per gallon of ...

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. The population standard deviation is 6 miles per gallon.
 a. With a .05 level of significance, test to determine whether or not the manufacturer's advertising campaign is legitimate.
 b. What is the p-value associated with the sample results?