STAT 420
Fall 2008
Homework #4
(10 points)
(due Friday, September 26, by 3:00 p.m.)
1.
Hogg and Ledolter report on an engineer in a textile mill who studies the effects
of temperature and time in a process involving dye on the brightness of a
synthetic fabric
(
brightness is measured on a 50-point scale
). Three observations
were taken at each combination of temperature and time.
Temperature
Time (cycles)
350
°
F
375
°
F
400
°
F
40
38, 32, 30
37, 35, 40
36, 39, 43
50
40, 45, 36
39, 42, 46
39, 48, 47
Construct the ANOVA table and conduct tests for the interaction first and then, if
appropriate, the main effects. Use
α
= 0.05 for each test.
[
R. V. Hogg and J.
Ledolter,
Applied Statistics for Engineers and Physical Scientists
, 2nd ed.
(
New
York: Macmillan, 1992
).
]
Brig <- c(38, 32, 30, 37, 35, 40, 36, 39, 43,
40, 45, 36, 39, 42, 46, 39, 48, 47)
Time <- c( 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2, 2)
Temp <- c( 1, 1, 1, 2, 2, 2, 3, 3, 3,
1, 1, 1, 2, 2, 2, 3, 3, 3)
summary(aov(glm(Brig ~ factor(Time) * factor(Temp))))
Df Sum Sq Mean Sq F value Pr(>F)
factor(Time) 1 150.222 150.222 9.6918 0.008968 **
factor(Temp) 2 80.778 40.389 2.6057 0.114863
factor(Time):factor(Temp) 2 3.444 1.722 0.1111 0.895749
Residuals 12 186.000 15.500
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1