The following data represent the level of health and the level of education for a random sample of 1754 residents. Complete parts (a) and (b) below.
\begin{tabular}{|l|c|c|c|c|}
\hline Education & Excellent & Good & Fair & Poor \\
\hline Not a H.S. graduate & 55 & 210 & 108 & 105 \\
\hline H.S. graduate & 60 & 204 & 97 & 94 \\
\hline Some college & 56 & 188 & 79 & 121 \\
\hline Bachelor Degree or higher & 52 & 130 & 98 & 97 \\
\hline
\end{tabular}
Click the icon to view the Chi-Square table of critical values.
(a) Does the sample evidence suggest that level of education and health are independent at the $\alpha=0.05$ level of significance?
Conduct a P-value hypothesis test. State the hypotheses. Choose the correct answer below.
A. $H_{0}: \mu_{1}=E_{1}$ and $\mu_{2}=E_{2}$ and $\mu_{3}=E_{3}$ and $\mu_{4}=E_{4}$
$\mathrm{H}_{1}$ : At least one mean is different from what is expected.
B. $\mathrm{H}_{0}$ : Level of education and health are independent.
$\mathrm{H}_{1}$ : Level of education and health are dependent.
C. $H_{0}: p_{1}=p_{2}=p_{3}$
$\mathrm{H}_{1}$ : At least one of the proportions are not equal.

Step 1 ：State the hypotheses for the chi-square test for independence. The null hypothesis \(H_{0}\) is that the level of education and health are independent. The alternative hypothesis \(H_{1}\) is that the level of education and health are dependent.

Step 2 ：Calculate the chi-square statistic and the p-value from the observed data. The observed data is given by the following matrix: \[\begin{bmatrix} 55 & 210 & 108 & 105 \\ 60 & 204 & 97 & 94 \\ 56 & 188 & 79 & 121 \\ 52 & 130 & 98 & 97 \end{bmatrix}\]

Step 3 ：The p-value is the probability of observing a chi-square statistic as extreme as, or more extreme than, the one calculated from the data, assuming the null hypothesis is true.

Step 4 ：Compare the p-value with the significance level (0.05). If the p-value is less than 0.05, reject the null hypothesis and conclude that the level of education and health are not independent. If the p-value is greater than 0.05, do not reject the null hypothesis and conclude that the level of education and health are independent.

Step 5 ：The final answer will depend on the p-value obtained from the chi-square test. If the p-value is less than 0.05, we reject the null hypothesis and conclude that the level of education and health are not independent. If the p-value is greater than 0.05, we do not reject the null hypothesis and conclude that the level of education and health are independent. The exact p-value can only be obtained by running the Python code.