91Ó°ÊÓ

$H_0$: The ratings given by Siskel and Ebert are not associated.

$H_a$: The ratings given by Siskel and Ebert are associated.

The following contingency table contains the expected frequencies corresponding to the

Observed frequencies

${(O-E)}^2$

•All expected frequencies are greater than 1, we can verify by referring to the above table.

• At most 20% of the expected frequencies are less than 5. In fact, none of the expected frequencies are less than 5, as we can verify by referring to the above table.

All assumptions are satisfied.

The test is to be performed at the 1% significance level, so$\mathrm{Î\pm }=0.01$.

$\raisebox{1ex}{${(O-E)}^2$}\!\left/ \!\raisebox{-1ex}{$E$}\right.$

the value of test statistic is${\mathcal{X}}^2=45.357$

the row variable has 3 values and column variable has 3 values, therefore r = 3, c = 3 and

$$\begin{gathered} {\mathcal{X}}^2=45.357df \\ =(r-1).(c-1) \\ =(3-1).(3-1) \\ =2×2 \end{gathered}$$

For, $\mathrm{Î\pm }=0.01$, Table VII reveals that the critical value is =4.

${{\mathcal{X}}_{0.01}}^2=13.277$

we see the test statistic falls in the rejection region. Thus we reject the test results are statistically significant at 1% level.

At the 1% significance level, the data provide sufficient evidence to conclude that the ratings associated by Siskel and Ebert are associated.