Math 160 - Cooley
Intro to Statistics
OCC
Section 9.2 – Critical-Value Approach to Hypothesis Testing
Test Statistic : The statistic used as a basis for deciding whether the null hypothesis should be rejected.
Rejection region : The set of values for the test statistic that leads to rejection of the null hypothesis.
Non-rejection region : The set of values for the test statistic that leads to non-rejection of the null hypothesis.
Critical values : The values of the test statistic that separate the rejection and non-rejection regions. A critical
value is considered part of the rejection region.
Rejection Regions for all possible tests :
Sign in Ha
Rejection region
Two-Tailed Test
≠
Both Sides
Left-Tailed test
<
Left Side
Right-Tailed Test
>
Right Side
Obtaining Critical Values
Suppose that a hypothesis test is to be performed at the significance level, . Then the critical value(s) must be
chosen so that, if the null hypothesis is true, the probability is  that the test statistic will fall in the rejection
region.
Some Important Values of z
z 0.10
z 0.05
z 0.025
z 0.01
z 0.005
1.28
1.645
1.96
2.33
2.575
 Exercises:
The curve in the following graphs is the normal curve for the test statistic under the assumption that the null
hypothesis is true. Determine the rejection region, the non-rejection region, the critical value(s), the
significance level, and identify the hypothesis test as a left-tailed, a right-tailed, or a two tailed test.
1)
2)
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Math 160 - Cooley
Intro to Statistics
OCC
Section 9.2 – Critical-Value Approach to Hypothesis Testing
 Exercises:
In the following exercises, determine the critical value(s) for a one-mean z-test. For each exercise, draw a graph
that illustrates your answer.
3)
A two-tailed test with   0.05 .
4)
A left-tailed test with   0.05 .
5)
A two-tailed test with   0.02 .
6)
A right-tailed test with   0.02 .
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