102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance. French Toast Men Women 47 65 Pancakes Waffles 35 59 28 55 Omelettes 53 60 Table 11.55 The null and alternative hypotheses for this test are, H0: Men and women select identical breakfasts. Ha: Men and women select different breakfasts. Level of significance, = .05 O E 2 ij ij 2 The test statistic, 2 ~ with r 1 c 1 DF E i 1 j 1 ij Where r and c be the number of rows and coloumns respectively. r c Expected count w.r.t. i j th cell, Eij Total of i th Row Total of j th Column Grand total The test statistic 2 = 4.013 Degrees of freedom = (2 - 1) (4 - 1) = 3 The p-value of this test, p = P (2 (3) > 4.013) = 0.2601 Since p-value = .2601 > .05, do not reject the null hypothesis. Therefore, at 0.05 level, the data provides no enough evidence to support the claim that men and women select different breakfasts. Use the previous information to make a graph of this situation. CLEARLY label and scale the horizontal axis and shade the region(s) corresponding to the p-value