Question

# Metalworks, a supplier of fabricated industrial parts, wants to determine if the average output rate for...

Metalworks, a supplier of fabricated industrial parts, wants to determine if the average output rate for a particular component is the same across the three work shifts. However, since any of four machines can be used, the machine effect must be controlled for within the sample. The accompanying table shows output rates (in units) for the previous day. (You will need to calculate the t-statistic, for the given α and df per the ANOVA Error row.)

 Machine (Factor B) Shift (Factor A) 1 2 3 A 1392 1264 1334 B 1228 1237 1107 C 1173 1108 1186 D 1331 1342 1387

a-1. Construct an ANOVA table

a-2. If significant differences exist across the machines, use Fisher’s LSD method at the 5% significance level to determine which machines have different average output rates. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

 MSE= 3362.806 df(error)= 6 number of treatments = 4 pooled standard deviation=Sp =√MSE= 57.990
 critical t with 0.05 level and 6 df= 2.447 Fisher's (LSD) =(t)*(sp*√(1/ni+1/nj) = 115.86
 Lower bound Upper bound differ (xi-xj ) ME (xi-xj)-ME (xi-xj)+ME μ1-μ2 139.333 115.857 23.48 255.19 significant difference μ1-μ3 174.33 115.86 58.48 290.19 significant difference μ1-μ4 -23.33 115.86 -139.19 92.52 not significant difference μ2-μ3 35.00 115.86 -80.86 150.86 not significant difference μ2-μ4 -162.67 115.86 -278.52 -46.81 significant difference μ3-μ4 -197.67 115.86 -313.52 -81.81 significant difference

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