8.4 The t-Test for One Sample

Let us revisit Exercise 6.5, where Sven claimed that the fuel consumption of his diesel car was less than 6.0 liters per 100 km. In the summer, he measured the following fuel consumptions in liters per 100 km:

In the exercise we were asked to determine if his claim was right. When I give this exercise to students after a lecture covering descriptive statistics, similar to how it was presented in Chapter 7, most course participants approach the exercise using descriptive statistics. They try to use the mean and standard deviation of the sample to answer the question. Typically, one half of a class concludes that Sven is right since the mean fuel consumption is below 6.0. The other half argues that, since some values are above 6.0, his claim must be incorrect. Although many students are hesitant to draw a definite conclusion, most are leaning towards one of these alternatives. They seldom claim that the question is wrongly posed.

Is it reasonable that researchers who are faced with the same problem and the same data arrive at completely different conclusions? Of course not, since the differences result from arbitrary and subjective considerations. After discussing this situation, some students revise their opinion and say that these data are insufficient to draw a conclusion.

Firstly, we might ask ourselves which number of measurements would be sufficient ...

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