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One sample t test for checking quality of motors

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See attached Excel file.

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 of automobile. It asks them to drive their cars until two tanks of gasoline have been used up and to record the mileage. The group then calculates and records the miles per gallon for each year. The data in the attached excel spreadsheet portray the results of the tests.

Questions

1. Formulate a statistical hypothesis appropriate for the consumer group's purpose.
2. Calculate the mean average miles per gallon. Compute the sample variance and sample standard deviation.
3. Construct the appropriate statistical test for your hypothesis, using a 0.05 significance level.

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Step by step method for computing test statistic for one sample t test is given in the answer.

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