1. Determine the null and alternative hypotheses.2. Specify the test statistic and its distribution if the null hypothesis is true.3. Select αand determine the rejection region.4. Calculate the sample value of the test statistic.5. State your conclusion.
3.4
Examples of
Hypothesis Tests
STEP-BY-STEP PROCEDURE FOR TESTING HYPOTHESES

Principles of Econometrics, 4t
h
Edition
Page 44
Chapter 3:
Interval Estimation and Hypothesis Testing
3.4.1a
One-tail Test of
Significance
The null hypothesis is
H
0
:
β
2
= 0
The alternative hypothesis is
H
1
:
β
2
> 0
The test statistic is Eq. 3.7
–
In this case
c
= 0, so
t
=
b
2
/se(
b
2
) ~
t
(
N
–
2)
if the null
hypothesis is true
Select
α
= 0.05
–
The critical value for the right-tail rejection region
is the 95
th
percentile of the
t-
distribution with
N
–
2 = 38 degrees of freedom,
t
(0.95,38)
= 1.686.
–
Thus we will reject the null hypothesis if the
calculated value of
t
≥ 1.686.
–
If
t
< 1.686, we will not reject the null hypothesis.
3.4
Examples of
Hypothesis Tests

Principles of Econometrics, 4t
h
Edition
Page 45
Chapter 3:
Interval Estimation and Hypothesis Testing
3.4.1a
One-tail Test of
Significance
Using the food expenditure data, we found that
b
2
= 10.21 with standard error se(
b
2
) = 2.09
–
The value of the test statistic is:
Since
t
= 4.88 > 1.686, we reject the null hypothesis
that
β
2
= 0 and accept the alternative that
β
2
> 0
–
That is, we reject the hypothesis that there is no
relationship between income and food expenditure,
and conclude that there is a
statistically significant
positive relationship between household income
and food expenditure
2
2
10.21
4.88
se
2.09
b
t
b
3.4
Examples of
Hypothesis Tests