738 / 762
738
Chapter 16: One-Way Analysis of Variance
The
F
critical value obtained from the output is
F
3
,
33
,
0.01
= 4.4368.
The table at the top of
Figure 16-17
is usually referred to as the
One –Way ANOVA Table. This involves computations on the
between (factor variability) and the within (error variability).
Define
= mean heat loss for mix 1;
= mean heat loss for mix 2;
= mean heat loss for mix 3;
= mean heat loss for mix 4.
The hypothesis testing write up using the classical approach for the test is
given next.
Using the information from the output, we can now present the hypothesis
test.
:
: Not all the population means are equal
:
F
= 38.9272
For a given significance level of 0.01, reject the null hypothesis if the
computed test statistic value of 38.9272 >
F
3, 33, 0.01
= 4.4368.
Conclusion
: Since 38.9272 > 4.4368, reject
H
0
. That is, at the 1%
significance level, there is a significant difference between the mean heat
loss through the bricks for the four different non-toxic chemical mixes.
The rejection region for the test is shown in
Figure 16-18
. Observe that the
test statistic value falls way to the right in the rejection region.