**Concepts Relating To Testing Of Hypotheses:**

Testing of hypotheses requires a researcher to be familiar with various
concepts concerned with it such as:

** ****Null
Hypothesis And Alternative Hypothesis:**

In the context of statistical
analysis, hypotheses are of two types viz., null hypothesis and alternative
hypothesis. When two methods A and B are compared on their relative
superiority, and it is assumed that both the methods are equally good, then
such a statement is called as the null hypothesis. On the other hand, if method
A is considered relatively superior to method B, or vice-versa, then such a
statement is known as an alternative hypothesis. The null hypothesis is
expressed as **H**_{0}, while the alternative
hypothesis is expressed as H_{a}. For example, if a researcher wants to test the hypothesis that the
population mean (μ) is equal to the hypothesized mean (H_{0}) = 100, then the null hypothesis
should be stated as the population mean is equal to the hypothesized mean 100.
Symbolically it may be written as:-

If sample results do not support
this null hypothesis, then it should be concluded that something else is true.
The conclusion of rejecting the null hypothesis is called as alternative
hypothesis H_{1}. To put it in simple words, the set of alternatives to the null
hypothesis is termed as the alternative hypothesis. If H_{0} is accepted, then it implies
that H_{a} is being rejected. On the other hand, if H_{0} is rejected, it means that H_{a} is being accepted. For H_{0}: μ = μ H_{0} = 100, the following three
possible alternative hypotheses may be considered:

Before the sample is drawn, the
researcher has to state the null hypothesis and the alternative hypothesis.
While formulating the null hypothesis, the following aspects need to be
considered:

1. Alternative hypothesis is usually
the one which a researcher wishes to prove, whereas the null hypothesis is the
one which he/she wishes to disprove. Thus, a null hypothesis is usually the one
which a researcher tries to reject, while an alternative hypothesis is the one
that represents all other possibilities.

2. The rejection of a hypothesis
when it is actually true involves great risk, as it indicates that it is a null
hypothesis because then the probability of rejecting it when it is true is α
(i.e., the level of significance) which is chosen very small.

3. Null hypothesis should always be
specific hypothesis i.e., it should not state about or approximately a certain
value.

**The
Level Of Significance:**

In the context of hypothesis testing, the level of
significance is a very important concept. It is a certain percentage that
should be chosen with great care, reason and insight. If for instance, the
significance level is taken at 5 per cent, then it means that H_{0}
would be rejected when the sampling result has a less than 0.05 probability of
occurrence when H_{0} is true. In other words,
the five per cent level of significance implies that the researcher is willing
to take a risk of five per cent of rejecting the null hypothesis, when (H_{0})
is actually true. In sum, the significance level reflects the maximum value of
the probability of rejecting H_{0}
when it is actually true, and which is usually determined prior to testing the
hypothesis.

**Test
Of Hypothesis Or Decision Rule:**

Suppose the given hypothesis is H_{0} and the alternative hypothesis H_{1}, then the researcher has to make
a rule known as the decision rule. According to the decision rule, the
researcher accepts or rejects H_{0}. For example, if the H_{0} is that certain students are good against the H_{1} that all the students are good,
then the researcher should decide the number of items to be tested and the
criteria on the basis of which to accept or reject the hypothesis.

**Type
I And Type II Errors:**

As regards the testing of
hypotheses, a researcher can make basically two types of errors. He/she may
reject H_{0} when it is true, or accept H_{0} when it is not true. The former is called as Type I error and the
latter is known as Type II error. In other words, Type I error implies the
rejection of a hypothesis when it must have been accepted, while Type II error
implies the acceptance of a hypothesis which must have been rejected. Type I
error is denoted by α (alpha) and is known as α error, while Type II error is
usually denoted by β (beta) and is known as β error.

**One-Tailed
And Two-Tailed Tests:**

These two types of tests are very
important in the context of hypothesis testing. A two-tailed test rejects the
null hypothesis, when the sample mean is significantly greater or lower than
the hypothesized value of the mean of the population. Such a test is suitable
when the null hypothesis is some specified value, the alternative hypothesis is
a value that is not equal to the specified value of the null hypothesis.