Level 4: Consider statistics as measures of qualities of a sample distribution.
4C
Predict and justify changes in a sampling distribution based on changes in properties of a sample (e.g., increase in the number of observations), or in the process generating the samples (e.g., some change that would influence the values of the sample statistic).
Students predict that the variability of a sampling distribution of percent red will change if the sample size is increased: "When we had 10 spins, it was rare to get 9 red and 1 blue. Now for 100 spins, we would need to see that 10 times, not one time, and that is very, very unlikely. So that’s why we won’t see 90% red for samples of 100 spins."
"If we change the structure of the spinner from 50% red to 60% red, the shape will shift to the right."
Anticipating Changes in a Sampling Distribution
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Expected Outcomes, Variability, and Sample Size
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Exploring how Properties of a Sample Impact a Sampling Distribution
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Making Sense of Changes to Sampling Distributions
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Lessons
5 Investigating Chance