Question

Problem #4: Consider the data set that is summarized in the Minitab Output below Source DF C2 Error 34 Total 36 Adj SS 86.12 104.98 191.10 Adj MS 43.06 3.09 F-Value 13.95 P-Value 0.000 S 1.157 R-Sq Level NMean 2 45.06% R-Sq ( adj) -41.83% StDev 9 8.4151.458 10 11.4012.106 18 7.807 1.681 Pooled StDev- 1.757 Fisher Individual Tests for Differences of Means Difference Difference of Levels Adjusted P-Value of Means 97。6667% CI T-Value (1.068, 4.903) 0.608(-2.312, 1.095) -3.594 (-5.239, -1.948) 2.985 simultaneous confidence level - 94.61% (a) Find a 93% Bonferonni confidence interval for 3- 2 (b) which pairs of means are significantly different (using the Bonferonni method at the 7% significance level)? enter your answer in the form a,b (numbers correct to 3 decimals) Problem #4(a) (A) 1 and 3 only (B) 2 and 3 only (C) 1 and 2 only (D) 1 and 2, 1 and 3 only (E) 1 and 2,2 and 3 only (F) all of them (G) 1 and 3, 2 and 3 only (H) none of them Problem #4(b): Select Which pairs?

Answer 1

Answer:

(a) 93%. C.1, for μ2-mis 14 8 14 8 = (-3.5646, 0.32861) where, yı = 9.721. y2= 8.103. M SE = 3.42, t0.07/ (2+3),34 = (b) 93%, С.I. for μ3-μι is 2.3750 15 8 15 8 (-41589, -03131) 93%, C.I. for μ3-μ.* MSE 14 15 14 (-2.2502, 1.0142 where, уз 7.485 From the above three con fidence interval s (including the con fidence interval for μ2-n) we see that C.I. for μ3-11 does not contain zero and contains all negative values hence we conclude that μ1 and μ3 are significantly different and μ1 > μ3