We'll start our exploration of hypothesis tests by focusing on population proportions. Specifically, we'll derive the methods used for testing:
- whether a single population proportion \(p\) equals a particular value, \(p_0\)
- whether the difference in two population proportions \(p_1-p_2\) equals a particular value \(p_0\), say, with the most common value being 0
Thereby allowing us to test whether two populations' proportions are equal. Along the way, we'll learn two different approaches to hypothesis testing, one being the critical value approach and one being the \(p\)-value approach.