Hypotheses

The first step in conducting a t-test is formulating the hypotheses. These hypotheses are the assumptions that we will confirm or reject. Two hypotheses are required: the null hypothesis and the alternative hypothesis.

For a t-test, the null hypothesis states: "The means of two samples are equal." The alternative hypothesis, in contrast, states: "The means of two samples are not equal."

The null hypothesis is denoted as H₀, and the alternative hypothesis is denoted as Hₐ.

If based on the t-test, we reject the null hypothesis, the alternative hypothesis is automatically accepted.

Another way to formulate an alternative hypothesis is as follows:

The latter form is used when:

1. You are certain that one group has either a higher or lower mean, but not the other way around. This applies to our heights example, where we can confidently state that, on average, females are not taller than males;
2. You are solely interested in determining if something is better. If it's not better, you don't care whether it's the same or worse. This is similar to a new website design. You only want to implement it if it's an improvement over the current one. If it's not, you'll stick with the current design until the new one is enhanced.