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.)

Homework Answers

Answer #1

ANSWER::

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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