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Chapter 15: Chi-Square Tests
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respectively.
: There was a change in the distribution of the proportions stated in
the null hypothesis for the second season.
.:
∑
( )
= 1.408
.: For a significance level 0.01, reject the null hypothesis if the
computed test statistic value,
2
= 1.408 >
= 11.345.
Conclusion
: Since 1.408 < 11.345, do not reject the null hypothesis.
That is, at the 1 percent level of significance, there is not enough sample
evidence to reject the postulated distribution of viewers who watch the four
reality shows given in the null hypothesis. That is, there does not seem to be
a significant change in the proportions of viewers for the second season
when compared to the first season.
Observe that the
P
-value = 0.7037. This
P
-value would support the decision
of not rejecting the null hypothesis since its value is greater than the
significance level of 0.01.
Figure 15-22
shows that the test statistic value falls in the do not reject
region for the test. This further supports the decision of failing to reject the
null hypothesis and to claim that there does not seem to be a significant
change in the proportions of viewers for the second seasonwhen
compared to the first season.