This document defines hypothesis testing and describes the basic concepts and procedures involved. It explains that a hypothesis is a tentative explanation of the relationship between two variables. The null hypothesis is the initial assumption that is tested, while the alternative hypothesis is what would be accepted if the null hypothesis is rejected. Key steps in hypothesis testing are defining the null and alternative hypotheses, selecting a significance level, determining the appropriate statistical distribution, collecting sample data, calculating the probability of the results, and comparing this to the significance level to determine whether to accept or reject the null hypothesis. Types I and II errors in hypothesis testing are also defined.

1. Hypothesis Testing
Mr Sathish Rajamani
Associate Professor
Ved Nursing College – Panipat
Definition
Hypothesis is a tentative predication or explanation of the relationship between two variables.
‘It implies there is a systematic relationship between two variables.
Basic Concepts Concerning Testing of Hypotheses
Null Hypotheses and Alternate Hypotheses: The null hypothesis is generally symbolized as
H0 and the alternative hypothesis as Ha. If we are to compare method A with method B about
its superiority and if we proceed on the assumption that both methods are equally good, then
this assumption is termed as the null hypothesis. As against this, we may think that the
method A is superior or the method B is inferior, we are then stating what is termed as
alternative hypothesis.
Suppose we want to test the hypothesis that the population mean (µ) is equal to the
hypothesised mean (µ H0 ) = 100.
Then we would say that the null hypothesis is that the population mean is equal to the
hypothesised mean 100 and symbolically we can express as:
H0: µ = µH0 = 100
If our sample results do not support this null hypothesis, we should conclude that something
else is true. What we conclude rejecting the null hypothesis is known as alternative
hypothesis. In other words, the set of alternatives to the null hypothesis is referred to as the
alternative hypothesis. If we accept H0, then we are rejecting Ha and if we reject H0, then we are
accepting Ha. For H0: µ = µ H0 = 100. we may consider three possible alternative hypotheses as
follows.

2. Alternative Hypothesis To be read as follows
Ha: µ ≠ µH0 The alternative hypothesis is that the population
mean is not equal to 100. i.e. it may be more or
less than 100.
Ha: µ > µ H0 The alternative hypothesis is that the population
mean is greater than 100
Ha: µ < µ H0 The alternative hypothesis is that the population
mean is less than 100
The level of significance: The level of significance is defined as the probability of rejecting a
null hypothesis by the test when it is really true, which is denoted as α. That is, P (Type I
error) = α.
Confidence Level: Confidence level refers to the possibility of a parameter that lies within a
specified range of values, which is denoted as c. Moreover, the confidence level is connected
with the level of significance. The relationship between level of significance and the
confidence level is c=1−α.
The common level of significance and the corresponding confidence level are given below:
 The level of significance 0.10 is related to the 90% confidence level.
 The level of significance 0.05 is related to the 95% confidence level.
 The level of significance 0.01 is related to the 99% confidence level.
Decision Rule: A decision rule spells out the circumstances under which you would reject
the null hypothesis.
Type – I and Type – II Error:
Decision
Reality
H0 - True H0 - False
Reject H0 Type – 1 Error Correct Decision
Accept H0 Correct Decision Type – 2 Error
A Type I error (sometimes called a Type 1 error), is the incorrect rejection of a true null
hypothesis. The alpha symbol, α, is usually used to denote a Type I error.
A Type II error (sometimes called a Type 2 error) is the failure to reject a false null
hypothesis. The probability of a type II error is denoted by the beta symbol β.
Two – Tailed and One – Tailed Tests:

3. The one-tailed test refers to a test of null hypothesis, in which the alternative hypothesis is
articulated directionally. Here, the critical region lies only on one tail. However, if the
alternative hypothesis is not exhibited directionally, then it is known as the two-tailed test of
the null hypothesis. Where in the critical region is one both the tails.
Procedure for Hypothesis Testing:
To test a hypothesis means to tell (on the basis of the data the researcher has collected)
whether or not the hypothesis seems to be valid. In hypothesis testing the main question is:
whether to accept the null hypothesis or not to accept the null hypothesis? Procedure for
hypothesis testing refers to all those steps that we undertake for making a choice between the
two actions i.e., rejection and acceptance of a null hypothesis. The various steps involved in
hypothesis testing are stated below:
1. Making a formal statement: The step consists in making a formal statement of the
null hypothesis (H0) and also of the alternative hypothesis (Ha). This means that
hypotheses should be clearly stated, considering the nature of the research problem.
2. Selecting Significance Level: The hypotheses are tested on a pre-determined level of
significance and as such the same should be specified. Generally, in practice, either 5% level
or 1% level is adopted for the purpose.
3. Deciding the Distribution to Use: After deciding the level of significance, the next
step in hypothesis testing is to determine the appropriate sampling distribution. The
choice generally remains between normal distribution and the t-distribution. The rules
for selecting the correct distribution are similar to those which we have stated earlier
in the context of estimation.

4. 4. Selecting a random sample and computing an appropriate value: Another step is
to select a random sample(s) and compute an appropriate value from the sample data
concerning the test statistic utilizing the relevant distribution. In other words, draw a
sample to furnish empirical data.
5. Calculation of the Probability: One has then to calculate the probability that the sample
result would diverge as widely as it has from expectations, if the null hypothesis were in fact
true.
6. Comparing the Probability: Yet another step consists in comparing the probability
thus calculated with the specified value for a , the significance level. If the calculated
probability is equal to or smaller than the a value in case of one-tailed test (and a /2 in
case of two-tailed test), then reject the null hypothesis (i.e., accept the alternative
hypothesis), but if the calculated probability is greater, then accept the null
hypothesis.
Reference:
1. C.R. Kothari, “Research Methodology Methods and Techniques”, 2nd edition,
New Age International Publishers, New Delhi. Page: 180 – 92.
2. www.statisticshowto.com/probability-and-statistics/hypothesis-testing/
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