A hypothesis is a statement made about the value of a population parameter, which can be tested by performing experiments or taking a sample from the population.

The result of the experiment or the statistic calculated from the sample is known as the test statistic.

To carry out the test, two hypotheses are formed:

- The null hypothesis (\(H_0\)), which is assumed to be correct,
- The alternate hypothesis (\(H_1\)), which gives information about the parameter if the assumption is shown to be wrong.

Tests can be one-tailed or two-tailed.

One-tailed tests have alternate hypotheses in the form \(H_1:p < x\) or \(H_1:p > x\).
Two-tailed tests have an alternate hypothesis in the form \(H_1:p \neq x\).

To carry out a hypothesis, you assume the null hypothesis to be true, then consider the probability of the observed value of the test statistic occurring.

If this probability is less than a given threshold, known as the significance level, then you reject the null hypothesis. The significance level to be used is stated in the question, and is typically 5%.

At the end of the test, make a concluding statement depending on whether you were able to reject the null hypothesis, in context of the problem.

If you rejected the null hypothesis:
There is sufficient evidence at the 5% significance level to reject the null hypothesis. It is likely that ...

If you were unable to reject the null hypothesis:
There is no evidence at the 5% significance level to reject the null hypothesis. There is no reason to believe that ...

Critical regions

If the test statistic falls within the critical region, you can reject the null hypothesis. The critical value is the first value to fall within the critical region.

For one-tailed tests, there is only one critical region, at either end of the probability distribution.
For two-tailed tests, there are two critical regions, at both ends of the probability distribution.

The actual significance level of a hypothesis test is the probability of incorrectly rejecting the null hypothesis.