1.The first step is to state the relevant null and alternative hypotheses. whether the alternative hypothesis can either be accepted or stays undecided as it was before the test.
2.The second step is to consider the statistical assumptions being made about the sample in doing the test; for example, assumptions about the statistical independence or about the form of the distributions of the observations.
3. Decide which test is appropriate, and stating the relevant test statistic.
4. Derive the distribution of the test statistic under the null hypothesis from the assumptions. For example, the test statistics may follow a Student's t distribution or a normal distribution.
5. The distribution of the test statistic partitions the possible values of T into those for which the null-hypothesis is rejected, the so called critical region, and those for which it is not.
6. Compute from the observations the observed value of the test statistic.
7. Decide to either fail to reject the null hypothesis or reject it in favour of the alternative. The decision rule is to reject the null hypothesis H0 if the observed value is in the critical region, and to accept or "fail to reject" the hypothesis otherwise.
February 15, 2018