In this lesson, students continue to analyze data from an experimental study. For this work, they recognize that a normal distribution can be used to model the simulated difference in means, so they can use areas under the normal curve to examine what they might consider sufficient evidence to draw a conclusion about the treatment from the experiment.

Students must reason abstractly and quantitatively (MP2) when they consider different levels of abstraction from the original data, including condensing the data into a difference of means, regrouping the data to find additional difference of means, examining the distribution of the differences of means, and comparing the original difference to the distribution. Students model with mathematics (MP4) when they approximate the distribution of simulated differences of means by using a normal distribution. Students are asked to find the area under a normal curve for certain values, which requires selection of appropriate tools (MP5).

The question of whether to use a one-tailed or two-tailed analysis is an important one in statistics, but beyond the scope of this course. All of the questions in these materials are designed to be analyzed using two-tailed analysis, although the results should be significant or not under either assumption.