This unit focuses on some important uses of randomization in statistics. Initially, students consider three types of study (experimental, observational, and survey) as ways of collecting data. In each form of study, random selection of participants and assignment into any subgroups is important for being able to generalize findings to a larger population. Students notice that an estimation of a proportion or mean of a population from sample data comes with some variability because different samples can result in different estimates. This can be expressed by including a margin of error along with any point estimates given.

Next, students examine the normal distribution as a common model for bell-shaped distributions. With technology, students can use a normal distribution model to approximate the proportion of data within certain intervals. This provides a way to quantify the confidence students should have in their estimates of population proportions or means. It also provides a way to check whether data from an experimental study has enough evidence to conclude that a difference in means between a control and treatment group is due to the treatment.

The unit concludes with an experimental study that students can do together, from study design to data collection and analysis. Then students draw a conclusion about the experiment based on their analysis.

Histogram from 16.5 to 25.5 by 0 point 5’s. Handspan, centimeters. Beginning at 16.5 up to but not including 17, height of bar at each interval is .001, .007, .013, .016, .052, .059, .087, .132, .159, .132, .104, .098, .069, .032, .023, .010, .004, .002, 0. A bell-curve line is drawn at the top of each of the bars across the graph.