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.

The test statistic for examining hypotheses about one population mean:

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 H0. 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:

They make it easier to reject null hypotheses.

where the observed sample mean, μ0 = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

Stating Your Research Questions and Hypotheses

The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen (hint: it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:

State Your Hypothesis: A Scientific Approach to A/B …

One of these statements must become the null hypothesis, and the other should be the . The null hypothesis contains equality. So for the above, the null hypothesis H0 : x = 98.6. It is common practice to only state the null hypothesis in terms of an equals sign, and not a greater than or equal to or less than or equal to.