Inference for Sampling (Lesson 4.4)
Chapter 4 - Day 5
Describe how to obtain a simple random sample using slips of paper or technology.
Explain the concept of sampling variability and the effect of increasing sample size.
Use simulation to test a claim about a population proportion.
Hopefully you saved a poster of your dotplot from Lesson 4.2, as you will need it for today’s lesson. In this lesson, students will create a new dotplot, this time taking random samples of size 10 instead of size 5. For this new dotplot, be sure to use the same scale on the x-axis as you did before. Also, be sure to have the “Crazy in Love” lyrics sheet available for students to use again.
Once again, we suggest playing some music while students work through the activity today.
Question #3 in the activity asks students “What does this dot represent?” The answer is “A random sample of 5 words, and an average calculated from that sample.” Point at a different dot and ask “What does this dot represent?” The answer is “A different random sample of 5 words, and an average calculated from that sample.” The dotplot represents many, many samples and an average calculated for each of those samples. The fact that each one of our samples produces a different estimate is the idea of sampling variability. Sampling variability is a critical concept for students to understand for when we later approach statistical inference. Here are a few ideas we are previewing in this lesson:
When calculating a confidence interval, we include a margin of error with our estimate because we know that estimates vary from sample to sample (sampling variability).
The P-value for a significance test tells us the probability (assuming H0 is true) of getting our observed result or more extreme, purely by chance due to sampling variability.
Notice that this lesson does not cover the third learning target about using simulation to test a claim about a population proportion. This idea can be discussed using exercises 15 – 18 from the textbook (we like #15).