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Question 744:

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:

Purchaser Miles per Gallon Purchaser Miles per Gallon
1 30.9 14 27.0
2 24.5 15 26.7
3 31.2 16 31.0
4 28.7 17 23.5
5 35.1 18 29.4
6 29.0 19 26.3
7 28.8 20 27.5
8 23.1 21 28.2
9 31.0 22 28.4
10 30.2 23 29.1
11 28.4 24 21.9
12 29.3 25 30.9
13 24.2

(a) Formulate a statistical hypothesis that accommodates the consumer groupÕs purpose.

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

(c) Conduct the appropriate statistical test of your hypothesis, using a .05 statistical significance level.

Need more than just an answer? Download the Easy t Excel T-test Calculator Package which gets you the answer with the detailed calculations.

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