Chapter 9: Introduction to Hypothesis Testing

384 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING
Suppose x 26 days. How we test the null hypothesis depends on the procedure we
used to establish the critical value. First, using the z-value method, we establish the following
decision rule:
Hypotheses
Decision Rule
H 0
: 25 days
H A
: 25 days
0.10
Test Statistic
A function of the sampled
observations that provides a basis
for testing a statistical hypothesis.
where:
If z z 0.10
, reject H 0
.
If z z 0.10
, do not reject H 0
.
z 0.10
1.28
Recall that the number of homes sampled is 64 and the population standard deviation
is assumed known at 3 days. The calculated z-value is called the test statistic.
The z-test statistic is computed using Equation 9.2.
z-Test Statistic for Hypothesis Tests for , Known
x
z
n
(9.2)
where:
x Sample mean
Hypothesized value for the population mean
Population standard deviation
n Sample size
Given that x 26 days, applying Equation 9.2 we get
Thus, x 26 is 2.67 standard deviations above the hypothesized mean. Because z is
greater than the critical value,
z 2.67 z 0.10
1.28, reject H 0
.
Now we use the second approach, which established (see Figure 9.4) a decision rule,
as follows:
Decision Rule
Then,
x
z 26
25
267 .
3
n
64
If x x 010 .
, reject H 0
;
Otherwise, do not reject H 0
.
If x 25. 48 days, reject H0;
Otherwise, do not reject H 0
.