illustrate the application of the t -test in the one-sample case, consider again the hybrid-vehicle problem mentioned earlier. With a sample of 100 vehicles, the researchers fi nd that the mean miles per gallon for the car is 52.5 mpg, with a standard deviation of 14. Do these results indicate the population mean might still be 50? In this problem, we have only the sample standard deviation ( s ). This must be used in place of the population standard deviation (s). When we substitute s for s, we use the t distribution, especially if the sample size is less than 30. We define t as

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illustrate the application of the t -test in the one-sample case, consider again the hybrid-vehicle problem mentioned earlier. With a sample of 100 vehicles, the researchers fi nd that the mean miles per gallon for the car is 52.5 mpg, with a standard deviation of 14. Do these results indicate the population mean might still be 50? In this problem, we have only the sample standard deviation ( s ). This must be used in place of the population standard deviation (s). When we substitute s for s, we use the t distribution, especially if the sample size is less than 30. We define t as
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