Unit 9: Sampling Distributions

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Connections

Exploratory Data Analysis
  • This unit begins with calculating a particular statistic for a sample (to make some inference about a population) and then to think about how that statistic might differ from sample to sample, so we go all the way back to basic exploratory data analysis.

  • Since this unit forces students to examine different types of distributions (sample, population and sampling distributions), students must revisit examining shapes, centers and spreads.

  • As stressed in previous units, it is crucial to label and title graphs properly so not to confuse a certain type of distribution with another.
Models
  • This unit uses models in different ways. For one, the Central Limit Theorem is built around the idea that the sampling distribution of the mean (for sufficiently large, independently drawn samples) follows the normal model.

  • Simulation models are another important part of this unit. It is important to simulate several samples to illustrate the idea behind sampling distributions.
Inference
  • This unit will be students’ first taste of what is involved when making formal inference about a population given a sample, so remind them of this end goal. It is important to foreshadow to students that sampling distributions (i.e. how our estimators might vary from sample to sample) are crucial in determining how far an estimate (sample statistic) differs from what we might expect under a given hypothesis and what this ultimately means.