Mileage. A recent research states that acetone added to the fuel tank in tiny amounts increases fuel efficiency in cars.

A random selection of 10 cars were driven, once without additives and a second time with acetone added. The results are recorded in the following table.

a) Find a 95% confidence interval for the mean mileage with no additive. Be sure to check the appropriate assumptions and conditions. Explain what your interval means.

b) Can we compute the 95% confidence interval for the mean increase in mileage with acetone added? Be sure to check the appropriate assumptions and conditions.

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Miles per Gallon Car # No additive Acetone 1 18.3 19.2 2 23.6 22.3 3 31.2 30.9 4 26.3 26.9 56 27.1 28.9 16.8 18.6 7 19.8 19.7 8 20.7 21.2 9 14.5 16.5 10 22.0 21.5