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Key_Assignment 2-spr2012

Key_Assignment 2-spr2012 - MGMT 405 Six Sigma Quality...

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MGMT 405: Six Sigma Quality Management Assignment 2 Solution 1. (a) Analysis of Variance Table for Service Source DF SS MS F P Teller 2 2.844 1.422 10.52 0.000 Error 33 4.459 0.135 Total 35 7.303 (b) Approximate .05,2,33 F by .05,2,30 3.32. F = Since F = 10.52 > 3.32, Reject Ho. Yes, at alpha = 5%, there is a significant difference in the mean service times for the three tellers. (c) Tukey's pairwise comparisons Family error rate = 0.0500 Individual error rate = 0.0196 Critical value = 3.47 Intervals for (column level mean) - (row level mean) 1 2 2 -0.9766 -0.2401 3 -0.9516 -0.3432 -0.2151 0.3932 From above computer output: For testing 0 1 2 H :μ =μ , the confidence interval (CI) of 1 2 μ μ - is (-0.9766, -0.2401). Since “0” is outside this CI, reject Ho . Also we see that 1 2 μ μ < . For testing 0 2 3 H :μ =μ , the confidence interval (CI) of 2 3 μ μ - is (-0.3432, 0.3932). Since “0” is inside this CI, do not reject Ho . Above two tests suggest that Teller 1 is the best since his/her mean service time is the smallest. However, since Teller 1 serves only drive-in customers, it may be justified to repeat the analysis based on Teller 1’s service times after asking him/her to serve walk-in customers.
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2. (a) Analysis of Variance for Time, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P System 2 103.333 103.333 51.667 56.36 0.000 Operator 4 64.667 64.667 16.167 17.64 0.000 Error 8 7.333 7.333 0.917 Total 14 175.333 (b) .05,2,8 4.46. F = Since F = 56.36 > 4.46, reject Ho. Yes, at alpha = 5%, there is a significant difference in the mean training times for the three systems. (c) Tukey 95.0% Simultaneous Confidence Intervals Response Variable Time All Pairwise Comparisons among Levels of System System = A subtracted from: System Lower Center Upper ----------+---------+---------+------ B -2.730 -1.000 0.7298 (-----*----) C 3.270 5.000 6.7298 (-----*----) ----------+---------+---------+------ 0.0 3.0 6.0 System = B subtracted from: System Lower Center Upper ----------+---------+---------+------ C 4.270 6.000 7.730 (-----*-----) ----------+---------+---------+------ 0.0 3.0 6.0 From above output: For testing 0 : , A B H μ μ =
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