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.

**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

A statement about the population, which contradicts the null
hypothesis, depending upon the situation, is called **alternative hypothesis**, which will be denoted
by *H*_{1}.

For example, if we test whether the population mean has a
specified value *μ*_{0}, then the null hypothesis would be
expressed as:

*H*_{0}:* μ = μ*_{0}

The alternative hypothesis may be formulated suitably as anyone of
the following:

(i) *H*_{1}:* μ ≠ μ*_{0}

(ii) *H*_{1}:* μ > μ*_{0}

(iii) *H*_{ 1}:* μ < μ*_{0}

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.

Tags : Statistics , 12th Statistics : Chapter 1 : Tests of Significance - Basic Concepts and Large Sample Tests

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12th Statistics : Chapter 1 : Tests of Significance - Basic Concepts and Large Sample Tests : Null Hypothesis and Alternative Hypothesis | Statistics

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