678 / 762
678
Chapter 15: Chi-Square Tests
Thus, we can now write the hypothesis test to determine whether or not
consumers have a preferred color for packaging
: There is no color preference for a specific packaging among consumers.
: There is a color preference for a specific packaging among consumers.
.:
=
∑
( )
= 11.4
.: For a significance level 0.05, reject the null hypothesis if the
computed test statistic value
= 11.4 >
= 9.488 (to three decimal
places).
Conclusion
: Since 11.400 > 9.488, reject the null hypothesis. That is, at the
5% level of significance, there is enough sample evidence to reject the null
hypothesis of no color preference for a specific packaging among
consumers. That is at the 5% significance level there is a color preference
for a specific packaging among the consumers.
Note
: The
P
-value = 0.0224 <
= 0.05, so we will have the same
conclusion if we use the
P
-value approach.
The shaded critical area is shown in
Figure 15-16
.