Question: Quality Motors is an automobile dealership that regularly advertises in its local market area. It claims that a certain make and model of car averages 30 miles to a gallon of gas and mentions that this figure may vary with driving conditions. A local consumer group wishes to verify the advertising claim. To do so, it selects a sample of recent purchasers of this make and model. It asks them to drive their cars until they have used two tanks of gas and to record the mileage. The group then calculates and records the miles per gallon for each car. Following are the results of the tests:

(a) Formulate a statistical hypothesis that accommodates the consumer group's purpose.

(b) Calculate the mean for miles per gallon. Compute the sample variance and sample standard deviation.