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?