Question: Utilize the following contingency table to answer the questions listed below.

              C₁           C₂

R₁           51          207

R₂          146         185

R₃          240         157

a. State the relevant null and alternative hypotheses.

b. Calculate the expected values for each of the cells.

c. Compute the chi-square test statistic for the hypothesis test.

d. Determine the appropriate critical value and reach a decision for the hypothesis test. Use a significance level of 0.05.

e. Obtain the p-value for this hypothesis test.