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47. A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Riem Amendment. The following table shows the results of the votes: Oppose Favor 1180 IUndecided 180 Sex Female Male TOTAL TOTAL 300 200 500 1150 At a = .05 using the p-value approach, test to determine if the votes cast were independent of the sex of the individuals.

Answer 1

Solution: The following cross tablulation have been provided. The row and column total have been calculated and they are shown below: Column 1 Column 2 Column 3 Total Row 1 180 300 200 Row 2 150 20 Total 330 The expected values are computed in terms of row and column totals. In fact, the formula is E.; = Rx where Ricorresponds to the total sum of elements in row i, C, corresponds to the total sum of elements in column, and T is the grand total. The table below shows the calculations to obtain the table with expected values: Expected Values Column 2 Total Column 1 5306300 = 198 339 200 = 132 Column 3 70x300 = 42 Row 1 100 300 = 60 300 Row 2 1000000 = 40 7030210 = 28 - 70 Total 330 100 Based on the observed and expected values, the squared distances can be computed according to the following formula: (E-0' E. The table with squared distances is shown below. Squared Distances Column 1 Column 2 Row 1 (180-198) = 1.636 (80-80) = 6.667 Column 3 (40-421 = 0.095 (50-28) = 0.143 Row 2 (150-132) 132 20-0019 = 10 -2.00 Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H: The two variables are independent H: The two variables are dependent This corresponds to a Chi-Square test of independence. Rejection Region Based on the information provided, the significance level is a = 0.05, the number of degrees of freedom is df = (2-1) (3-1) = 2, so then the rejection region for this test is R = {x? :x>5.991). Test Statistics The Chi-Squared statistic is computed as follows: (0- Ej) = 1.636 +2.455 +6.667 +10+ 0.095 +0.143 = 20.996 - 1636 2.455 +6.667 + 10 Eij

Decision about the null hypothesis Since it is observed that x = 20.996 > x = 5.991, it is then concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level The corresponding p-value for the test is p = Pr(xi > 20.996) = 0.