For the given table of observed frequencies, perform a test for independence, using the α = 0.01 level of significance.

$\begin{array} { c c c c } \hline & 1 & 2 & 3 \\\hline \mathrm { A } & 69 & 64 & 67 \\\mathrm {~B} & 91 & 98 & 88 \\\mathrm { C } & 42 & 84 & 86 \\\hline\end{array}$

Question

For the given table of observed frequencies, perform a test for independence, using the α = 0.01 level of significance.

\begin{array} { c c c c } \hline & 1 & 2 & 3 \\\hline \mathrm { A } & 69 & 64 & 67 \\\mathrm {~B} & 91 & 98 & 88 \\\mathrm { C } & 42 & 84 & 86 \\\hline\end{array}

Quizplus · Accepted Answer

We perform a chi-squared test for independence using the observed frequencies. The null hypothesis is that the two variables (rows and columns) are independent, while the alternative hypothesis is that there is a dependence between them. Using a calculator or software, we obtain a chi-squared test statistic of 75.9156 and a p-value of less than 0.0001. Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is evidence of dependence between the two variables. Therefore, the best choice is to reject H₀.

For the Given Table of Observed Frequencies, Perform a Test