Experience First

Chapter 7 provides the foundation for the remainder of the course, where students will tackle statistical inference (confidence intervals and significance tests). To truly understand inference, students need a good fundamental understanding of sampling distributions. At its core, the idea is that every random sample will produce slightly different results (sampling variability) and we want to think about the distribution of possible results. By the end of the chapter, we will be able to describe the shape, center, and variability for two sampling distributions: sample proportions and sample means.

 

In this lesson, we start with the simplified scenario of a very small population (5 students) and taking samples of size 2. In the second more realistic scenario, we have a population of 40 students and we are taking samples of size 5. You will need sticker dots and a poster prepared for question #6. 

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Formalize Later

This activity is truly an Experience First, Formalize Later (EFFL) design, as students can complete the entire activity without knowing any fancy vocabulary or notation. It is in the debrief where the new vocabulary (sampling distribution) and notation (xbar) will be introduced. 

 

When debriefing #3 in the activity, be sure to ask students “What does this dot represent?”

 

The first dotplot truly is a sampling distribution, because all of the possible samples of size 2 are represented. Technically speaking, the second dotplot is not a true sampling distribution because it does not have all possible samples of size 5 (there are 40C5 = 658,008 of them!) But this second dotplot is already starting to give us a good idea what the distribution of sample means will look like, and we are comfortable labeling it as the “Sampling Distribution of xbar”. 

 

The third learning target asks students to use a sampling distribution to evaluate a claim and is not covered in the activity. Students first saw this idea in Lesson 4.4 and will see it in the Check Your Understanding.