Hypothesis Testing Using Test Statistics or Using Probabilities

There are two ways we can conduct a hypothesis test. Iwill illustrate with an example from the normal distribution assuminga two tailed test.

Using a Test Statistic

We have a null distribution anda single observation We find Supposewe are conducting a 5% test. We find a test statistic andcorresponding to 5% – assuming a two tailed test - bycalculating andlooking up the corresponding value of inthe normal distribution table, we find Ifthe value of z we found using isbigger than this we reject the null hypothesis.

Using a Probability

We have a null distribution anda single observation We find Supposewe are conducting a 5% test. Everything so far is as it was above.But now, instead of finding the test statistic corresponding to 5% -assuming a two tailed test – we use the calculated value of z tofind a probability. If the probability we find is less than 2.5%- sincewe are conducting a two tailed test - we reject the nullhypothesis.

Things to Remember

Big test statistic implies reject null hypothesis and small teststatistic implies do not reject null hypothesis.

Small probability implies reject null hypothesis and bigprobability implies do not reject null hypothesis.

The test statistic is related to the probability of the nullhypothesis being true – if the test statistic is large theprobability of the null hypothesis being true is small, so reject thenull hypothesis - if the test statistic is small the probability ofthe null hypothesis being true is large so do not reject the nullhypothesis.