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Unit 12: Hypothesis Testing

3. A ………………test is one in which the test statistics leading to rejection of null hypothesis Notes
falls on both tails of the sampling distribution curve as shown.
4. ………………tells the researcher the number of elements that can be chosen freely.

12.3 Errors in Hypothesis Testing

There are two types of errors:
1. Hypothesis is rejected when it is true.
2. Hypothesis is not rejected when it is false.
(1) is called Type 1 error (a), (2) is called Type 2 error ( b). When a =0.10 it means that true
hypothesis will be accepted in 90 out of 100 occasions. Thus, there is a risk of rejecting a true
hypothesis in 10 out of every 100 occasions. To reduce the risk, use a = 0.01 which implies that we
are prepared to take a 1% risk i.e., the probability of rejecting a true hypothesis is 1%. It is
also possible that in hypothesis testing, we may commit Type 2 error (b) i.e., accepting a null
hypothesis which is false.

Notes The only way to reduce Type 1 and Type 2 error is by increasing the sample size.

Example of Type 1 and Type 2 error:

Type 1 and Type 2 error is presented as follows. Suppose a marketing company has 2 distributors
(retailers) with varying capabilities. On the basis of capabilities, the company has grouped them
into two categories (1) Competent retailer (2) Incompetent retailer. Thus R 1 is a competent
retailer and R2 is an incompetent retailer. The firm wishes to award a performance bonus (as a
part of trade promotion) to encourage good retailership. Assume that two actions A1 and A2
would represent whether the bonus or trade incentive is given and not given. This is shown as
follows:
Action (R1) Competent retailer (R2) Incompetent retailer
A 1 performance bonus is Correct decision Incorrect decision error ()
awarded
A 2 performance bonus is not Incorrect decision error () Correct decision
awarded

When the firm has failed to reward a competent retailer, it has committed type-2 error. On the
other hand, when it was rewarded to an incompetent retailer, it has committed type-1error.

12.4 Types of Tests

1. Parametric test.
2. Non-parametric test.

12.4.1 Parametric Test

(1) Parametric tests are more powerful. The data in this test is derived from interval and ratio
measurement.
(2) In parametric tests, it is assumed that the data follows normal distributions. Examples of
parametric tests are (a) Z-Test, (b) T-Test and (c) F-Test.

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