Module 3 Inference for Proportion

This module introduces statistical inference through the study of proportions, focusing on how sample data can be used to make claims about a population. Students begin by reviewing the concept of sampling distributions and the central limit theorem (CLT) for sample proportions. They learn the conditions under which the CLT applies and how it helps approximate the distribution of sample statistics.

The module explains key terms such as sample proportion (\(\hat{p}\)), population proportion (\(p\)), point estimate, and error, emphasizing how sampling error and bias affect estimation. Through examples like opinion polls, learners explore how point estimates summarize population characteristics and how uncertainty decreases as sample size increases.

Students also examine the sampling distribution of the sample proportion, understanding that when sample sizes are large and conditions are met, the distribution of \(\hat{p}\) approaches normality. The module includes step-by-step examples (e.g., estimating support for immigration using survey data) and interactive exercises that demonstrate how to compute and interpret sample proportions.

By the end of this unit, students will be able to:

Calculate and interpret point estimates for population proportions.

Understand sampling variability and its connection to the central limit theorem.

Differentiate between random error and bias in estimation.

Apply statistical reasoning to make population-level inferences based on sample data.