\fMath 1368 Ho Decision Chi-Square & F Lab Name Make a p-value sketch then find the p-value rounding to 4-decimal places followed by your Ho decision. Assume conditions are met and use a= 0.05. 1) Ho The 2-categorical variables are independent. 5) HOW = H, = H H. The 2-categorical variables are dependent. H, At least one of the means is different. 7= = 10.023 df = 12 0= 0.05 F = 2.576 n = 28 k=4 p-value sketch p-value sketch p-value OF Num DF Den _ p-value Conclusion: Conclusion: 2) Ho The 2-categorical variables are independent. 6) HOM = = = Ha H. The 2-categorical variables are dependent. H, At least one of the means is different. 72 = 24.057 of = 17 0= 0.05 F= 4.318 n=17 k=7 p-value sketch p-value sketch p-value OF Num OF Den _ p-value Conclusion: Conclusion: 3) Ho The proportions are the same. H. At least one of the proportions is different. 7) HOM = M; = 1: H, At least one of the means is different. 72 = 12.376 df = 5 0= 0.05 F = 5.368 n=19 k=11 p-value sketch p-value p-value sketch Conclusion: OF Num OF Den __ p-value Conclusion: 4) Ho The proportions are the same. H. At least one of the proportions is different. H, At least one of the means is different. 72 = 17.569 di = 8 0= 0.05 F = 1.877 n=31 k=17 p-value sketch p-value p-value sketch Conclusion: OF Num OF Den p-value Condusion