9
-1
Hypothesis Testing
Chapter 9 Learning Objectives
LO 9.1
Define the null hypothesis and the alternative hypothesis.
LO 9.2
Distinguish between Type I and Type II errors.
LO 9.3
Conduct a hypothesis test using the
p
-value approach.
LO 9.4
Conduct a hypothesis test using the critical value
approach.
LO 9.5
Differentiate between the test statistics for the
population mean.
LO 9.6
Specify the test statistic for the population proportion.

9
-2
9.1 Introduction to Hypothesis Testing
Hypothesis tests:
is the testing of a hypotheses (generally established
ideas, beliefs or claims.)
In a hypothesis test, define
H
0
, the
null hypothesis
, the default belief or status quo
(established hypothesis).
H
A
, the
alternative hypothesis
, a contradiction of the default believe or
status quo.
Example: Prior research finds that the average weekly income of graduated
workers is $1200. A new researcher claims that
it is different. The null and
alternative hypotheses are:
H
0
: µ= $1200
H
A
: µ≠$1200

9
-3
Hypothesis Testing
Use the following signs in hypothesis tests
specify the status quo,
contradict
H
0
.
Note that
H
0
always contains the “equality.”
H
0
=
>
<
H
A
≠
<
>
9.1 Introduction to Hypothesis Testing
On the basis of sample information, we can either
“
Reject the null hypothesis
”
Sample evidence
is
inconsistent with
H
0
.
“
Do not reject the null hypothesis
”
Sample evidence
is not
inconsistent with
H
0
.

9
-4
One tailed test:
is when
H
A
includes > or < symbols.
Example:
If the general belief is that the average life expectancy in most developing countries
is less than or equal to
70 years, but a researcher claims that it is
more than
70 years, then
9.1 One-Tailed versus Two-Tailed
Hypothesis Tests
H
0
:
<
versus
H
A
:
>
(
right-tail test
)
On the other hand, if the general belief is that the average life expectancy in most developed
countries is greater than or equal to 70, but a researcher claims that it is
less than
70 years then
H
0
:
>
versus
H
A
:
<
(
left-tail test
)
Note that the inequality in
H
A
determines which tail area will be
used to make the decision regarding the rejection of
H
0
.

9
-5
9.1 One-Tailed versus Two-Tailed Hypothesis
Tests
A
one-tail hypothesis test
is used when the alternative
hypothesis is stated as < or >
Right tail test
: reject the null
hypothesis, if the test result is in
the yellow area as indicated
below, otherwise do not reject.
Reject
H
0
Reject
H
0
Reject
H
0
Do not reject
H
0
Reject
H
0
0
H
Do not reject
H
0
Left tail test
: reject the null
hypothesis if the test result is in
the yellow area as indicated
below, otherwise do not reject.