Statistics and Probability
Material Type:
Community College / Lower Division, College / Upper Division
Central Limit Theorem, Sample Mean, Sample Proportion, Sampling Distribution
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Education Standards (1)

Sampling Distributions and Central Limit Theorem

Module Overview

Ideally a census will be able to provide answers to many questions about a population. However, a census is impractical in many ways. So we need to rely on information drawn from a carefully chosen random sample of individuals/objects from the population. Such information may include sample statistics - proportion, mean, median, standard deviation, correlation, distribution, etc. The downside of the sampling approach is that the information we get is bound to change when we take a different sample. Then how can we ensure that we can make reliable inference about the population using only the sample information we got from our sample? The answer lies in the sampling distribution of the statistic which allows us, under certain assumptions, to make predictions about its values. These predictions, in turn, can be compared with the actual values obtained in the sample.

Learning Objectives:

  • Sampling Distribution of the Sample Mean
  • Sampling Distribution of the Sample Proportion
  • Central Limit Theorem, its assumptions and conclusion.


Textbook Material - 

  • Chapter 7 – The Central Limit Theorem – Pages 395 – 401, 405 – 413

Suggested Exercises – Chapter 7 – Odds 61 – 71, 76 – 93

    Section 1: Chapter Exercises

    Suggested Exercises – Chapter 7 – Odds 61 – 71, 76 – 93

    Please see Instructor Facing Content 

    Section 2: Class Worksheet

    Insert class worksheet here 

    Please see Instructor Facing Content 

    Section 3: Lab

    Section 4: Key Terms