Week 7 / Module 6 — Sampling Distributions

An ordered list of subtopics covered in Module 6, including sampling distributions, population parameters vs. sample statistics, the Central Limit Theorem, and related concepts, used to give learners and instructors an at-a-glance overview of the module's curriculum.

A landing page for Module 6 that links learners to the core resources for the module, including the PowerPoint slide deck, lecture video, and a Google Colab code demonstration of the Central Limit Theorem.

A reading page that explains key Module 6 concepts in depth, covering the Central Limit Theorem and its implications, the sampling distribution of the mean, and related inference topics, serving as a primary reference text to support the lecture and other materials.

This reading introduces the concept of sampling distributions, explaining how they serve as the theoretical link between sample observations and conclusions about a population, laying the groundwork for tools like confidence intervals and hypothesis tests.

This reading clarifies the distinction between population parameters (fixed, usually unknown values describing an entire group) and sample statistics (values calculated from a subset), explaining how statistics are used to estimate parameters and why that distinction matters in engineering and research contexts.

This reading explains the Central Limit Theorem, describing how the distribution of sample means approaches normality as sample size increases regardless of the population's original shape, and why this result makes probability calculations about sample means tractable in practice.

This reading examines how increasing sample size reduces the variability of sample statistics, covering the standard error concept and explaining why larger samples produce more precise and reliable estimates of population parameters.

This reading covers how to correctly interpret and apply sampling distributions in practice, distinguishing between distributions of individual values and distributions of statistics, and guiding learners through using sampling distributions to answer probability questions and make inferences about populations.

A 45-question quiz bank assessing learners on sampling distribution concepts such as applying the Central Limit Theorem to non-normal populations, calculating standard error, and interpreting hypothesis testing outcomes, used by instructors to build graded quizzes.

A graded discussion assignment in which learners prompt an AI with questions about sampling concepts and then reflect on the AI's response, encouraging critical engagement with the importance of using samples to make statistical predictions and decisions.

A graded assignment in which learners construct and interpret 90%, 95%, and 99% confidence intervals for a population proportion using survey data from a tech company's user satisfaction study, applying sampling and inference skills.