Sampling Distributions

Grade 9•45 minutes•Act as a responsible and contributing community members and employee. Utilize critical thinking to make sense of problems and persevere in solving them. Use technology to enhance productivity increase collaboration and communicate effectively. MP.1 Make sense of problems and persevere in solving them MP.2 Reason abstractly and quantitatively MP.3 Construct viable arguments and critique the reasoning of others MP.4 Model with mathematics MP.5 Use appropriate tools strategically MP.6 Attend to precision MP.7 Look for and make use of structure MP.8 Look for and express regularity in repeated reasoning S.ID.A.4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Supporting (Algebra 2) S.IC.A.1. (+) Understand statistics as a process for making inferences about population parameters based on a random sample from that population. S.IC.A.2. (+) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. S.IC.B.4. (+) Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. S.CP.B.7. (+) Apply the Addition Rule, P(A or B) = P(A)+P(B)-P(A and B), and interpret the answer in terms of the model.

Learning Objective

I can describe how the mean of a sampling distribution, the corresponding population mean, and the population proportion are related.

Practice Questions

This lesson includes 6 practice questions to reinforce learning.

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1. Define "sampling distribution" in your own words, and explain what it represents.

2. Explain the difference between a population parameter and a sample statistic. Give an example of each.

3. In the video's example with the balls numbered 1, 2, and 3, the population mean was calculated. If instead, we wanted to know the population proportion of even numbers, what would that proportion be? How would you estimate this proportion using samples of size 2 (with replacement)?

...and 3 more questions

Educational Video

Introduction to sampling distributions | Sampling distributions | AP Statistics | Khan Academy

Khan Academy

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