Consider the following contingency table, which records the results obtained for four samples of fixed sizes selected from four populations.

a. Write the null and alternative hypotheses for a test of homogeneity for this table.
b. Calculate the expected frequencies for all cells assuming that the null hypothesis is true.
c. For α = .025, find the critical value of x2. Show the rejection and non-rejection regions on the chi-square distribution curve.
d. Find the value of the test statistic x2.
e. Using α = .025, would you reject the null hypothesis?

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Sample Selected From Row 1 Row 2 Row 3 Population 1 24 46 20 Population 2 81 64 37 Population 3 60 91 105 Population4 121 72 93