Statistical inference consists of estimation of parameters and testing of hypotheses. Estimation has already been discussed this content is about the testing of hypotheses. Point estimation and interval estimation as discussed earlier have their own fields of application. Sometimes there is a situation in which the point estimation and the interval estimation are either not required or the estimation of parameters does not provide any inference. For example, the following situations require inference which is not possible by methods of estimation.
- The contents of a medicine have been changed to improve the effectiveness of the medicine. In this situation both the point estimation and the interval estimation fail to answer the question about the improvement of the medicine. In this case we have to take help from the sample data to decide whether or not the medicine has been improved.
- A manufacturer of tires claims that the average life of his tires is at least 15000 kilometers. The life of tires is an important factor to settle the price of the tires. It is big information if we prove with reasonable amount of confidence that the life of the tires is not more than 15000 kilometers. The answer is not provided by a point estimate or by an interval estimate of the life of the tires. What we shall have to do is that we shall examine the claim of the manufacturer on the basis of the experiment conducted on the sample of tires. A certain procedure will be adopted to reach some conclusion. This is what we shall call the test of hypothesis about the life of tires.