How do you perform a Statistical Hypothesis Testing?

To start with you select your hypothesis and its opposite: the null and alternative hypotheses. You select a confidence level (alpha %), which is the probability that your testing procedure rejects the null hypothesis when, if fact, it is true.

Next you select a test statistic and calculate its probability distribution under the two hypotheses. You then find the possible values of the test statistic which, if the null hypothesis were true, would only occur alpha % of the times. This is called the critical region.

Carry out the trial and collect data. Calculate the value of the test statistic. If it lies in the critical region then you reject the null hypothesis and go with the alternative hypothesis. If the test statistic does not lie in the critical region then you have no evidence to reject the null hypothesis.