Page 458 - Six Sigma Demystified

438 Six SigMa DemystifieD

CHIDIST((20-1)*(15^2)/(21^2),20-1)). When the p value is less than 0.05, we
reject the null hypothesis and can assert the alternative hypothesis (i.e., the
strong conclusion).
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68. b. The F statistic for testing equality of variance is calculated (for s > s >) in
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Excel as =(21^2)/(15^2).
69. d. In Excel, the p value for the two-sided hypothesis that the variances are equal
is 0.15, calculated as P=2*FDIST((21^2)/(15^2),20-1,20-1). When the p value
exceeds 0.05, we fail to reject the null hypothesis. Choice c is incorrect because
we cannot assert the alternative (because this is the weak conclusion of failing to
reject); we can only suggest that there are insufficient data to reject the null
hypothesis.
70. d.
71. d.
72. c.
73. b.
74. c.
75. d.
76. b.
77. d.
78. c.
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79. d. Note the X term.
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80. a. Choice b is incorrect because there are no higher-order terms. Choice c may
not be correct if there are no extra runs (degrees of freedom) to calculate error
because only four trials are used.
81. d. F tests cannot be performed on the regression when there are insufficient
degrees of freedom (unique trials or experimental conditions) to estimate error.
Often, factors can be removed from the regression to free up trials for error
estimation.
82. d. Standard notation for designed experiments where there are n factors all at L
levels is Ln.
83. b. Increasing the number of observations by replicating an experiment provides

the benefits described by i and iii. Note that ii is untrue and that only choice b
doesn’t have ii.
84. b.
85. a.
86. d. Taguchi and Plackett-Burman designs are screening designs that involve a large
number of factors with a small number of trials. Response surface designs
attempt to fit a nonlinear equation to the response surface. This requires more
degrees of freedom than a screening experiment. EVOP is used to make gradual
improvements over time. A large number of trials is made; then very small
changes are made in the factor levels.
87. b.
88. d.
89. d.
90. a. Interaction AB will be at its low level, AC at its high level, and ABC at its low
level.