A bhypothesis/b is a statement made about the value of a bpopulation parameter/b, 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 btest statistic/b.

To carry out the test, two hypotheses are formed:

• The bnull hypothesis/b ((H_0)), which is assumed to be correct,
• The balternate hypothesis/b ((H_1)), which gives information about the parameter if the assumption is shown to be wrong.

Tests can be one-tailed or two-tailed.

bOne-tailed/b tests have alternate hypotheses in the form (H_1:p < x) or (H_1:p > x).
bTwo-tailed/b 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 bless than/b a given threshold, known as the bsignificance level/b, 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:
iThere is sufficient evidence at the 5% significance level to reject the null hypothesis. It is likely that .../i

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

bCritical regions/b

If the test statistic falls within the bcritical region/b, you can reject the null hypothesis. The bcritical value/b 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 bactual significance level/b of a hypothesis test is the probability of incorrectly rejecting the null hypothesis.