6 Inference

Previously, we learned how to generate random variables according to many different distributions. And we also learned two important theorems – the law of large numbers (LLN) and the central limit theorem (CLT). Now in this chapter, we will learn how to reach statistical conclusions based on a given dataset.

Learning Objectives

• Learn how to calculate and interpretate confidence intervals based on the dataset.
• Learn how to perform a hypothesis test, including one-sample test, two-sample test, and a test for proportions.
• Learn how to perform a chi-squared test.

Useful Functions

• Use z.test() to calculate confidence intervals when population standard deviation is known.

• Use t.test() to calculate confidence intervals when population standard deviation is not known.

• Use prop.test() to get approximate result for tests for proportions.

• Use binom.test() to get exact result for tests for proportions only applied for one-sample questions.

• Use power.z.test() to calculate the critical value where we would reject the null if we observe data more extreme than that.

• Use chisq.test() to test for dependence between the row and column variables.