Page 209 - Computational Statistics Handbook with MATLAB

196 Computational Statistics Handbook with MATLAB

is based on whether the value of the test statistic falls in the rejection region.
We will discuss an alternative method later in this section. The concepts of
hypothesis testing using the critical value approach are illustrated in Exam-
ple 6.2.

PROCEDURE - HYPOTHESIS TESTING (CRITICAL VALUE APPROACH)

1. Determine the null and alternative hypotheses.
should be
2. Find a test statistic T that will provide evidence that H 0
accepted or rejected (e.g, a large value of the test statistic indicates
should be rejected).
H 0
3. Obtain a random sample from the population of interest and com-
using the sample.
pute the observed value of the test statistic t o
4. Using the sampling distribution of the test statistic under the null
hypothesis and the significance level, find the critical value(s). That
is, find the t such that

Upper Tail Test: P H T ≤( t) = 1 – α
0
Lower Tail Test: P H T ≤( t) = α
0
Two-Tail Test: P H T ≤( t 1 ) = α 2 and P H T ≤( t 2 ) = 1 – α , 2 ⁄
⁄
0 0
where P H .() denotes the probability under the null hypothesis.
0
falls in the critical region, then
5. If the value of the test statistic t o
reject the null hypothesis.

Example 6.2
Here, we illustrate the critical value approach to hypothesis testing using the
transportation example. Our test statistic is given by

x – µ 0
z = -------------- ,
σ
X
and we observed a value of z = 1.47 based on the random sample of
o
n = 100 commute times. We want to conduct the hypothesis test at a signif-
icance level given by α = 0.05. Since our alternative hypothesis is that the
commute times have increased, a large value of the test statistic provides evi-
dence for H . We can find the critical value using the MATLAB Statistics
1
Toolbox as follows:
cv = norminv(0.95,0,1);

© 2002 by Chapman & Hall/CRC