10.55 Midsized cars’ gas mileage change Refer to the previous exercise. Statistics of the change in the overall performance and the city performance are summarized in the following table:

a. Explain how this standard deviation could be so much less than the standard deviations for the miles per gallon (mpg) performance for each test alone.

b. Is 10 mpg a plausible mean change in the population of midsized cars? Answer by constructing a 95% confidence interval for the population mean change in mpg or conducting a significance test of the hypothesis that the mean mpg change in the population equals 10. Interpret.

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n Mean Std. Dev. Difference 15 8.93 1.79 (Overall - City)