# Null and Alternative Hypotheses for a Mean

So, you might get a *p*-value such as 0.03 (i.e., *p* = .03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where *p* = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance.

## All null hypotheses include an equal sign in them.

### Formally we do not reject the null hypothesis.

A statistical **hypothesis test** is a procedure for deciding between two possible statements about a population. The phrase **significance test** means the same thing as the phrase "hypothesis test."

### Formally we reject the null hypothesis.

When you set up a hypothesis test to determine the validity of a statistical claim, you need to define both a null hypothesis and an alternative hypothesis.

## Stating a hypothesis in a research paper - Advantages …

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.

## Stating Hypotheses In Research Paper - …

Every hypothesis test contains a set of two opposing statements, or hypotheses, about a population parameter. The first hypothesis is called the denoted H_{0}. The null hypothesis always states that the population parameter is to the claimed value. For example, if the claim is that the average time to make a name-brand ready-mix pie is five minutes, the statistical shorthand notation for the null hypothesis in this case would be as follows:

## A research hypothesis is the statement created by researchers when ..

Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the **mean** exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the **distributions**, **medians**, amongst other things. As such, we can state: