12-2. Ho: X = X2 = X3 = X4; HA: At least one mean is not equal to the other three means.
F - Statistic = 5.91; Fcrit = 3.24; = 0.05; P Value = 0.0065
Since the P -- Value is less than the alpha value, we reject the null hypothesis.
There is insufficient evidence that all four samples have equal means.
12-7.
a. Ho: X = X = X3; HA: At least one mean differs significantly from the other means F - Statistic = 5.03; Fcrit = 3.89; a = 0.05; P - Value = 0.026 Since the P -- Value is less than the alpha value, we reject the null hypothesis. There is insufficient evidence to suggest that all three groups have equal means.
b.
K = 3 groups; df = n - k = 15 - 3 =12; Qk=3; df-12; a=0.os = 3.773; MSE =1.6736 HSD1;2 = 3.773V ((1.6736/2) (0.2+0.25)) = 2.3153 HSD1;3 = 3.773 V (0.8368(1/5 +1/6)) = 2.0899 HSD2:3 = 3.773 V (0.8368(1/4 + 1/6)) = 2.2279 1 - 2 = 2.75 > 2.3153 = HSD1;2; Significant 1 - 3 = 1.33 > 2.0899 = HSDi;3; Not Significant 2 - 3 = 1.42 > 2.2279 = HSD2:3; Not Significant The difference between Group 1 and Group 2 is significan