9.2: Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.

The null hypothesis, denoted by H₀ is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As a result if you cannot accept the null, it requires some action.

The alternative hypothesis, denoted by H₁ or H_a, is a claim about the population that is contradictory to H₀ and what we conclude when we reject H₀. This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, one must examine evidence to determine whether e to reject the null hypothesis or not. The evidence used is in the form of sample data.

After deciding which hypothesis the sample data supports, a decision can be made. There are two options for a decision. They are "reject H₀" if the sample information favors the alternative hypothesis or "do not reject H₀" or "decline to reject H₀" if the sample information is insufficient to reject the null hypothesis.

This text is adapted from Openstax, Introductory Statistics, Section 9.1 Null and Alternative Hypothesis

Hypothesis testing begins with stating at least two contrasting statements of a claim about a population characteristic.

Consider an example of studying the proportion of healthy and scabbed apples from a cultivar.

To test this, we may begin by stating that 'the cultivar produces an equal number of healthy and scabbed apples.' This statement is the null hypothesis, denoted as H₀, and is represented as follows.

Alternatively, the statement that 'the cultivar produces a different proportion of the healthy and scabbed apples' has an opposite viewpoint than the previous one. This statement is the alternative hypothesis, denoted as H₁, and is represented as follows.

An alternative hypothesis should not state that the parameter value equals an exact number or a predetermined fixed value.

For instance, 'proportion of scabbed apples harvested from the cultivar is 0.2' is not an appropriate alternative hypothesis as one may get that exact value of proportion just by chance alone but may not get enough data to support the claim of proportion being precisely 0.2.