• Non-directional (2-tailed test): In this form of the test, departure can be observed from either end of the distribution. Thus, no direction for expected results are specified. The null and alternative hypotheses are as follows:

• Directional (1-tailed test): In this form of the test, the rejection region lies at only one end of the distribution. The direction is specified before any analysis begins.

  

The nature of the null and alternative hypotheses determines the conclusions that you can make about the results of your study. For example, in a two-tailed study, you are constrained to conlcude that the two samples differed significantly (if you reject the null). In a one-tailed study, however, you are entitled to make statements saying that one group did significantly better or worse than the other.

Confidence intervals can be calculated as follows:

The z set of formulas is used on sampling distributions, not on population distributions. Thus, as N approaches infinity, your sampling distribution will approach normality, regardless of the shape of the parent population distribution (central limit theorem).