Page 54 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 3: Language of Research

3.4.1 Hypothesis Testing Notes

A number of steps are involved in testing a hypothesis:
i. Formulate a hypothesis
ii. Set up a suitable significance level
iii. Choose a test criterion

iv. Compute the statistic
v. Make decision.
 Formulate a Hypothesis: Let us discuss about introduction of a new drug. The drug is
tested on a few patients and based on the response from patients, a decision has to be made
whether the drug should be introduced or not. We make certain assumptions about the
parameter to be tested – these assumptions are known as hypotheses.
We start with a ‘null hypothesis’: H : m = 100. This is a claim or hypothesis about the
0
values or population parameter.
This is tested against alternate hypothesis, H : m  100.
1
The null hypothesis is tested with available evidence and a decision is made whether to
accept this hypothesis or reject it. If the null hypothesis is rejected, we accept the alternate
hypothesis.
 Setting up a Suitable Significance Level: There are two types of errors that can be committed
in making decisions regarding accepting or rejecting the null hypothesis:
 Type I error: An error made in rejecting the null hypothesis, when in fact it is true.
 Type II error: An error made in accepting the null hypothesis, when in fact it is
untrue.

Did u know? What is level of significance?
The level of significance signifies the probability of committing Type I error and is
generally taken as equal to 5% (a = .05).

This means that even after testing the hypothesis, when a decision is made, we may still be
committing 5% error in rejecting the null hypothesis when it is actually true. Sometimes,
the value of ‘a’ is taken as .01 but it is the discretion of the investigator, depending upon
the sensitivity of the study.
 Choose a Test Criterion: This means selection of a suitable test statistic that can be used
along with the available information carrying out the test. The different test statistics that
are normally used are:

 Normal Distribution: z-statistic, this is most often used, when the samples are more
than 30.

 t-statistic: ‘t’ test is used for small samples only.
 F-statistic
 Chi-Square statistic.
 Compute the Test Characteristic: This involves the actual collection and computation of
the sample data. For the case under consideration, we have to find the sample mean () and

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