A null hypothesis is an assumption that is used to deny or affirm an event in relation to some or some parameters of a population or sample.
Whenever a conclusion is reached about an experiment, the researcher must establish two hypotheses, the null hypothesis and the alternative hypothesis. The null hypothesis (H0) refers to the contrary statement that the researcher has reached. It is the hypothesis that the researcher intends to reject. If you have enough evidence for this, you can prove that the opposite is true. Therefore, the alternative hypothesis (H1) is the conclusion that the researcher has reached through his research.
The statement of the null hypothesis cannot be rejected unless the sample data seems to prove that it is false. In general, the null hypothesis includes a no (or an unequal a) in its statement.
Regarding the above, it is worth explaining why it is called the null hypothesis. One of the first studies on which it was applied was on the effect of fertilizers on crops. The starting hypothesis (null hypothesis) was that the fertilizer had no effect. Therefore, if the null hypothesis was rejected, it meant that they did have an effect.
Example of null hypothesis formulation
Suppose a researcher has conducted an investigation about the average monthly salary per inhabitant in a given neighborhood of a city. Imagine that the researcher has surveyed 1,000 people, concluding that the average monthly salary per inhabitant is CU1,500
Therefore, the researcher wants to contrast, if that average monthly salary per inhabitant is equal to CU1,500 (conclusion of the study and therefore alternative hypothesis) or if, on the contrary, the average monthly salary per inhabitant is different from CU1,500 (conclusion contrary to of the study to be denied and therefore null hypothesis)
The contrast to be made would be the following:
H0: The average monthly salary is different from 1,500 um
H1: The monthly salary is equal to 1,500 um
As a result, we have the formulation of the two hypotheses that the researcher intends to test. It is important to realize (as commented in the second paragraph of the explanation) that the null hypothesis, refers just to the idea contrary to what has been reached with the investigation.
As a mnemonic rule to know how to establish the null hypothesis, we must always think about what we need to validate the conclusion of our research. If our investigation concludes that the average monthly salary is equal to CU1,500, what do we need to validate the conclusion of our investigation?
We need to reject the opposite. This is that the average monthly salary is different from CU1,500 (H0). In this way we could affirm that the average monthly salary is equal to CU1,500 (H1).
Conclusions of the hypothesis contrast of the example
After the contrast made, the researcher may or may not reject the null hypothesis (thus proving that the alternative hypothesis is true). The correct thing to comment on the result of a hypothesis test is always to speak in terms of the null hypothesis.
If the hypothesis has been rejected, the following statement can be used, “in the light of the data and after the result obtained through the hypothesis test, sufficient evidence is available to reject the null hypothesis.”
Therefore, the conclusion would be that the average monthly salary is equal to um 1,500. On the contrary, if the null hypothesis of the contrast made could not be rejected, the following statement could be used, “in the light of the data and after the result obtained through the contrast of hypotheses made, there is not enough evidence to be able to reject the null hypothesis ”. If so, the conclusion would be that the average monthly salary is not equal to um 1,500