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

                                              Sample Selected From

              Popualation 1         Popualation 2       Popualation 3         Popualation 4

Row 1             24                        81                      60                        121

Row 2             46                        64                      91                         72

Row 3             20                        37                     105                         93

a. Write the null and alternative hypotheses for a test of independence for this table.

b. Calculate the expected frequencies for all cells, assuming that the null hypothesis is true.

c. For α =.01, find the critical value of χ2. Show the rejection and nonrejection regions on the chi-square distribution curve.

d. Find the value of the test statistic χ2 .

e. Using α =.01, would you reject the null hypothesis?