http://www.chem1.com/acad/webtext/matmeasure/mm5.html

Very well written and clear account of how Normal distribution and Confidence Intervals are used for making decisions.

Here is a sample:

3 Using statistical tests to make decisions

Once we have obtained enough information on a given sample to evaluate parameters such as means and standard deviations, we are often faced with the necessity of comparing that sample (or the population it represents) with another sample or with some kind of a standard. The following sections paraphrase some of the typical questions that can be decided by statistical tests based on the quantities we have defined above. It is important to understand, however, that because we are treating the questions statistically, we can only answer them in terms of statistics— that is, to a given confidence level.

The usual approach is to begin by assuming that the answer to any of the questions given below is “no” (this is called the

*null hypothesis*), and then use the appropriate statistical test to judge the validity of this hypothesis to the desired confidence level.