In this module, you will explore how probability distributions can help us approximate and understand statistical inference. You will compare bootstrap and randomization approaches and discover the connection between confidence intervals and hypothesis tests. Using the Normal distribution, you will learn to calculate p-values and confidence intervals while developing a deeper understanding of what these results tell us about a population. You will also learn to distinguish statistical significance from practical significance, an essential skill for deciding whether a result is meaningful beyond simply being statistically detectable. By considering sample size, replication, and study limitations, you will develop the ability to evaluate how reliable a statistical conclusion is and recognize when the evidence may not support a strong claim.

In this module, you will bring together the tools of statistical inference to answer questions about populations and differences between groups. You will learn how to select the appropriate inferential procedure for proportions, means, differences between groups, and paired data, then construct and interpret confidence intervals and hypothesis tests to evaluate what the data can tell us. You will also explore how the Normal and t-distributions, standard error, and the Central Limit Theorem provide the foundation for making these inferences. You will apply these methods to real statistical questions, using p-values and confidence intervals to evaluate claims and distinguish meaningful evidence from chance variation. Throughout the module, you will use R to conduct common inferential analyses, including one- and two-sample tests for proportions and means and paired t-tests. You will also learn to use graphical checks to assess assumptions, helping you make informed and reliable conclusions from statistical data.

In this final module, you will review the core concepts of confidence intervals, hypothesis testing, and statistical inference covered throughout the course. This review provides an opportunity to bring together the key ideas, methods, and interpretation skills you have developed and prepare to apply them independently. You will then complete the Final Exam, which evaluates your understanding of statistical inference and your ability to apply these concepts to statistical questions. Use this final assessment to demonstrate what you have learned and your ability to interpret statistical evidence with confidence.