National open university of nigeria introduction to econometrics I eco 355

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100 
3.4. Testing the significance of 
The Chi Square (
Test
As another illustration of the test-of-significance methodology, consider the following 
variables 
̂
which, as noted previously, follows the x 2 distribution with n – 2 df. For the hypothetical 
example, 
̂
= 42.1591 and df = 8. If we postulate that 
= 85 vs. 
, Eq. 
(4.4.1) provides the test statistic for 
. Substituting the appropriate values in (4.4.1), it 
can be found that under 
= 3.97. If we assume 
= 5%, the critical 
values are 
2.1797 and 17.5346. Since the computed 
lies between these limits, the data support 
the null hypothesis and we do not reject it. This test procedure is called the chi-square test 
of significance. 
1. The Logic of Hypothesis Testing
As just stated, the logic of hypothesis testing in statistics involves four steps. We 
expand on those steps in this section:
First Step: State the hypothesis
Stating the hypothesis actually involves stating 
two opposing hypotheses
about the value 
of a population parameter.
Example
: Suppose we have are interested in the effect of prenatal exposure of alcohol on 
the birth weight of rats. Also, suppose that we know that the mean birth weight of the 
population of untreated lab rats is 18 grams.
Here are the two opposing hypotheses:

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101 
o
The Null Hypothesis (Ho).
This hypothesis states that