# 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 hypotheses -- 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).

### State Null and Alternative Hypotheses

A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.

### State Null and Alternative Hypotheses

The first step in hypothesis testing is to set a research hypothesis. In Sarah and Mike's study, the aim is to examine the effect that two different teaching methods – providing both lectures and seminar classes (Sarah), and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and Mike's 50 students. More specifically, they want to determine whether performance is different between the two different teaching methods. Whilst Mike is skeptical about the effectiveness of seminars, Sarah clearly believes that giving seminars in addition to lectures helps her students do better than those in Mike's class. This leads to the following research hypothesis:

### In, we stated null and alternative hypotheses:

Generally, when comparing or contrasting groups (samples), the null hypothesis is that the difference between means (averages) = 0. For categorical data shown on a contingency table, the null hypothesis is that any differences between the observed frequencies (counts in categories) and expected frequencies are due to chance.