Hypothesis testing is an important branch of statistics . It is one of the two branches of inferential statistics .

The first step in hypothesis testing involves estimating population parameters. The estimates of the population parameters are usually given by sample statistics, such as sample mean and sample variance. The sampling strategy  and the statistical estimation of sample statistics preceedes hypothesis testing stage.

Hypothesis testing, also known as the second type of inference, involves the definitions of a hypothesis as one set of possible population values and an alternative, a different set. There are many statistical procedures for determining, on the basis of a sample, whether the true population characteristic belongs to the set of values in the hypothesis or the alternative.

It is more important to understand the testing procedures in practical terms than doing the arithmatic to arrive at a conclusion. The mathematical calculations relating to the testing procedures are simple and easy to define mathematically.  However a decission maker should be familir with the implications of the conclusion arrived from the hypothesis testing.

We shall try to understand these issues below.

Null Hypothesis (H0) means nothing is changed or nothing is present. Some example null hypotheses are: a new process hasn't produced any faulty products; and a new medical treatment hasn't shown any negative impact on a group of malaria patients etc. Not rejecting H0 does not necessarily mean one accepts the null hypothesis, since not rejecting H0 does not prove H0 is true.

Basically the tests are designed to look for evidence to reject H0. When not enough evidence is available one does not reject H0. Obvioulsy there are cases at which one might wrongly reject H0 when it is true.

For examaple the error of wrongly rejecting a lot when it actually meets the minimum agreed standards. In statistical testing this type of error is called Type-I error (or alpha risk). This is also known as producer's risk.

Alternative Hypothesis (H1) is that the process or treatment has an effect. the Type-II error is the error of not rejecting H0 when it is false. It is the error of passing a lot when it does not meet the minimum standards. This is known as consumer's risk. One usually decides the significance level (type-I error) of the test prior to conducting the test.

Obviously if the investigator is a product manufacturer he would like to reduce the type-I error. However this will usually result in increased type-II error, if the sample size used to conduct the test is fixed.

So for a fixed sample size the investigator needs to make an informed decision about fixing the significance level of the test. If it is possible the investigator should consider increasing the sample size to reduce the probabilities of both types of error.

The following table summarizes the hypothesis testing and the errors associated with it.

	Decision: Problem	Decision: No Problem
Fact:  No Problem	Type-I Error (alpha): Risk of rejecting a good lot Risk of convicting an innocent	alpha - one hundred percent: Chance of accepting a good lot Chance of acquitting an innocent
Fact:  Problem	Power of the test (gamma): Chance of rejecting a bad lot Chance of convicting the guilty	Type-II Error (beta): Risk of accepting a bad lot Risk of acquitting the guilty

Now we shall discuss the test-statistic for a variety of statistical testing procedures.

Test for the mean: Let us suppose that the unknown population mean is the same as the mean of the sample derived from that population. In this case our null hypothesis is that the population mean is equal to the sample mean, and our alternative hypothesis is that the population mean is quite different from the sample mean. Remember this test requires the following assumptions to be valid: 1) The population is normal, unless the sample size is more than 30.

Hypothesis testing plays an important role in Business Statistics and statistical Information Techniques .