Lesson 1: 7.1 What is a Sampling Distribution?
Duration of Days: 2
Lesson Objective
Students will be able to distinguish between parameters and statistics and understand that a sampling distribution represents the values of a statistic from all possible samples of the same size from the same population.
How can we distinguish between the "true" value of a population and the "estimate" we get from a sample?
If every student in this class takes a random sample of 10 people, why will we all get different results?
What does it mean for a statistic to be an "unbiased estimator"?
Parameter
Statistic
Sampling Distribution
Distribution of a Sample
Unbiased Estimator
Variability of a Statistic
HSS-IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
HSS-IC.B.4: Use data from a sample survey to estimate a population mean or proportion.
Questions often ask if a result can be generalized to a population. Understanding that a sample statistic is merely an estimate of the population parameter is the logic behind every SAT survey question.
The goal is to help students realize that while a single sample might be "off," the collection of all possible samples follows a very predictable, often normal-shaped pattern.
The Problem: A large jar contains thousands of beads; 60% are red (p = 0.60). A teacher has students take 500 different random samples of size n = 20 and calculate the proportion of red beads in each.
Task A: Describe the center, shape, and spread of the resulting distribution values.
Task B: If a student got a sample with only 10% red beads, would that be a "surprising" result? Explain.
Sample Size vs. Number of Samples
Mixing up Symbols
Students struggle to distinguish between the distribution of the population, the distribution of one sample, and the sampling distribution.
Support: Use the "S-P Mnemonic." Statistics come from Samples; Parameters come from Populations.
Extension: Have advanced students explore "Biased Estimators." Ask them why we use n-1 when calculating sample variance instead of just n.
Kinesthetic: Use a "human dot plot." Have every student draw a sample of 5 pennies, calculate the average year, and physically stand in a line to form the sampling distribution.
Teacher assigns examples from the textbook and other resources.
Access E-Book through Classlink