# How to Set Up a Hypothesis Test: Null versus Alternative

We usually set the hypothesis that one wants to conclude as the alternative hypothesis, also called the research hypothesis. The above example is about population proportion and thus we set up the hypotheses in terms of .

## For all three alternatives, the null hypothesis is o: = o.

### State Null and Alternative Hypotheses

Notice that the alternative hypothesis is **"proved" indirectly** by obtaining **strong enough evidence** to reject the lack of effect stated by the null hypothesis.

### How do we decide whether to reject the null hypothesis?

When debating the State Appropriation for Penn State, the following question is asked: "Is the majority of students at Penn State from Pennsylvania?" To answer this question, we can set it up as a hypothesis testing problem and use data collected to answer it.

## Learn About Null Hypothesis and Alternative Hypothesis

Before moving onto the second step of the hypothesis testing process, we need to take you on a brief detour to explain why you need to run hypothesis testing at all. This is explained next.

## Null and Alternative Hypothesis | Real Statistics Using …

If the drought plants wilt and die but the watered plants flower and set seed, then the null hypothesis is rejected in favor of the reasonable alternative.

## Alternative Hypothesis: Definition

The (or hypothes*es* -- there may be more than one) is our working hypothesis -- our prediction, or what we expect to happen. It is also called the - because it is an alternative to the null hypothesis. Technically, the claim of the research hypothesis is that with respect to the outcome variable, our samples are from *different* populations (remember that refers to the group from which the sample is drawn). If we predict that math tutoring results in better performance, than we are predicting that after the treatment (tutoring), the treated sample truly is different from the untreated one (and therefore, from a different population).