The website fueleconomy.gov allows drivers to report the miles per gallon of their vehicle. The data in Table 3 show the reported miles per gallon of 2011 Ford Focus automobiles for 16 different owners. Treat the sample as a simple random sample of all 2011 Ford Focus automobiles. Construct a 95% confidence interval for the mean miles per gallon of a 2011 Ford Focus. Interpret the interval.

Approach

Step 1 Verify the data are obtained randomly and the sample size is small relative to the population size. Because the sample size is small, draw a normal probability plot to verify the data come from a population that is normally distributed and a boxplot to verify that there are no outliers.

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By-Hand Approach Step 2 Compute the value of x and s. Step 3 Determine the critical value to with n 1 degrees of freedom. Step 4 Use Formula (2) to determine the lower and upper bounds of the confidence interval. Step 5 Interpret the result.