NULL HYPOTHESIS AND ALTERNATIVE HYPOTHESIS
In many practical studies, as mentioned earlier, it is necessary to make decisions about a population or its unknown characteristics on the basis of sample observations. For example, in bio-medical studies, we may be investigating a particular theory that the recently developed medicine is much better than the conventional medicine in curing a disease. For this purpose, we propose a statement on the population or the theory. Such statements are called hypotheses.
Thus, a hypothesis can be defined as a statement on the population or the values of the unknown parameters associated with the respective probability distribution. All the hypotheses should be tested for their validity using statistical concepts and a representative sample drawn from the study population. ‘Hypotheses’ is the plural form of ‘hypothesis’.
A statistical test is a procedure governed by certain determined/derived rules, which lead to take a decision about the null hypothesis for its rejection or otherwise on the basis of sample values. This process is called statistical hypotheses testing.
The statistical hypotheses testing plays an important role, among others, in various fields including industry, biological sciences, behavioral sciences and Economics. In each hypotheses testing problem, we will often find as there are two hypotheses to choose between viz., null hypothesis and alternative hypothesis.
A hypothesis which is to be actually tested for possible rejection based on a random sample is termed as null hypothesis, which will be denoted by H0.
A statement about the population, which contradicts the null hypothesis, depending upon the situation, is called alternative hypothesis, which will be denoted by H1.
For example, if we test whether the population mean has a specified value μ0, then the null hypothesis would be expressed as:
H0: μ = μ0
The alternative hypothesis may be formulated suitably as anyone of the following:
(i) H1: μ ≠ μ0
(ii) H1: μ > μ0
(iii) H 1: μ < μ0
The alternative hypothesis in (i) is known as two- sided alternative and the alternative hypothesis in (ii) is known as one-sided (right) alternative and (iii) is known as one-sided (left) alternative.