Hypothesis Testing - Introduction

The primary goal of hypothesis testing is to decide whether to reject the null hypothesis. If the null hypothesis is rejected, it means there is enough evidence to support the alternative hypothesis. If it is not rejected, it means there isn't enough evidence to support the alternative, rather than saying the alternative is false.

A hypothesis is a claim about a population parameter. There are two main types: the null hypothesis (Ho), which always contains equality, and the alternative hypothesis (Ha or H1), which is the complement of the null and never contains equality. The alternative hypothesis determines whether a test is one-tailed or two-tailed. For example, if the claim is that the mean is equal to 23, Ho: µ = 23, and Ha: µ ≠ 23 (two-tailed test). If the claim is that the mean is less than 23, Ha: µ < 23, and Ho: µ ≥ 23 (left-tailed test).

To decide when to reject the null hypothesis, a significance level (alpha, commonly 0.05) is selected. This alpha specifies the size of the critical or rejection region. For a two-tailed test, alpha is divided into both tails. For one-tailed tests (left or right), alpha is not divided, and the rejection region is entirely in one tail. If the calculated test statistic falls within this rejection region, the null hypothesis is rejected; otherwise, it is not rejected.