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.