Making the Case for Normality<br>In a variety of settings, students in AP Statistics are asked to make a judgment about whether or not the assumption that a given sample has been drawn from a normal distribution is a reasonable one. For example, on the 2001 AP Statistics Exam (problem 5), students were asked to provide statistical evidence about the difference in the active ingredients in two brands of pills. To use the appropriate t-statistic as part of their solution, they needed to assess whether the distribution of difference appeared to be a normal distribution, given that the sample size was only 10. The best solutions presented a graphical display of the sample distribution along with a statement that is was reasonable to assume that the underlying distribution of differences is normal. In this article, I'll look at what students in an introductory course can do to make the case for the normality of the population and note the limitations of these procedures.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education