Module 4 Inference for Mean

This module builds on foundational statistical concepts by introducing inference for a population mean using the t-distribution. It begins with a review of the Central Limit Theorem (CLT) and the conditions under which the sample mean \(\bar{x}\) can be modeled as approximately normal. When the population standard deviation \(\sigma\) is unknown, the t-distribution is used instead of the normal distribution, with degrees of freedom \((df = n -1)\) determining its shape.

Key learning objectives include:

Differentiating between normal and t-distributions.

Constructing confidence intervals for one sample and paired samples.

Performing hypothesis tests for a single mean and for paired data.

Students learn to:

Check conditions for inference (independence and normality).

Use sample statistics \(\bar{x}\) and \(s\) to estimate population parameters.

Apply the t-distribution to calculate standard errors, critical values, and p-values.

Interpret results in context, including confidence intervals and hypothesis test conclusions.