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. The population standard deviation is 6 miles per gallon. Required:
a. State the hypotheses.
b. What is the p-value associated with the sample results? With a 0.05 level of significance, test to determine whether or not the manufacturer's advertising campaign is legitimate.