91Ó°ÊÓ

Consider the given question,

According to the null and alternative hypotheses,

$H_0$denotes race distributions among the four U.S. regions are homogeneous.

$H_{\mathrm{Î\pm }}$denotes race distributions among the four U.S. regions are non-homogeneous.

The level of significance is $\mathrm{Î\pm }=0.01$.

On finding the expected frequency and test statistics,

Pearson Chi-square$=11.520,$

$$\begin{gathered} df=2, \\ p-value=0.003 \end{gathered}$$

Therefore, the value of Pearson chi-square is $11.520$.

Therefore, the p-value is$0.003$.

Consider the rejection rule,

If $P-value≤\mathrm{Î\pm }$, then reject the null hypothesis.

Here, the P-value is lesser than the level of significance, $P-value\left(=0.003\right)<\mathrm{Î\pm }\left(=0.01\right)$

Therefore, the null hypothesis is rejected at $1\%$level.

The results are statistically significant at the above given level of significance.

Hence, the data provide sufficient evidence to conclude that a difference exists in a proportions of supporters among the three regions at the $1\%$significance level.