Page 239 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes Hypothesis testing is sometimes called confirmatory data analysis, in contrast to exploratory
data analysis. In frequency probability, these decisions are almost always made using null-
hypothesis tests; that is, ones that answer the question. Assuming that the null hypothesis is
true, what is the probability of observing a value for the test statistic that is at least as extreme
as the value that was actually observed? One use of hypothesis testing is deciding whether
experimental results contain enough information to cast doubt on conventional wisdom.

12.1 Meaning of Hypothesis

A hypothesis is a tentative proposition relating to certain phenomenon, which the researcher
wants to verify when required.
If the researcher wants to infer something about the total population from which the sample was
taken, statistical methods are used to make inference. We may say that, while a hypothesis is
useful, it is not always necessary. Many a time, the researcher is interested in collecting and
analysing the data indicating the main characteristics without a hypothesis. Also, a hypothesis
may be rejected but can never be accepted except tentatively. Further evidence may prove it
wrong. It is wrong to conclude that since hypothesis was not rejected it can be accepted as valid.
What is a Null Hypothesis?

A null hypothesis is a statement about the population, whose credibility or validity the researcher
wants to assess based on the sample.
A null hypothesis is formulated specifically to test for possible rejection or nullification. Hence
the name ‘null hypothesis’. Null hypothesis always states “no difference”. It is this null hypothesis
that is tested by the researcher.

12.2 Statistical Testing Procedure

1. Formulate the null hypothesis, with H and HA, the alternate hypothesis.
0
According to the given problem, H represents the value of some parameter of population.
0
2. Select on appropriate test assuming H to be true.
0
3. Calculate the value.

4. Select the level of significance other at 1% or 5%.
5. Find the critical region.
6. If the calculated value lies within the critical region, then reject H .
o
7. State the conclusion in writing.

12.2.1 Formulate the Hypothesis

The normal approach is to set two hypotheses instead of one, in such a way, that if one hypothesis
is true, the other is false. Alternatively, if one hypothesis is false or rejected, then the other is true
or accepted. These two hypotheses are:
(1) Null hypothesis
(2) Alternate hypothesis
Let us assume that the mean of the population is µo and the mean of the sample is x. Since we
have assumed that the population has a mean of µo, this is our null hypothesis. We write this as

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