STAT 496, Spring 2004
Homework Assignment #4
1. In an experiment on the effectiveness of laundry detergents, 2 brands of detergent and 2 water temperatures are used in a 22 factorial experiment. A standard load of laundry consists of 2 pairs of jeans,
5 sets of cotton underwear, 5 pairs of white crew socks, 5 cotton shirts, and 3 cotton towels. Each
load is mixed with 100 grams of top soil, shaken to remove loose dirt, and weighed. Five standard
laundry loads are washed for each of the combinations. One washing machine is used and the order of
the twenty loads is completely randomized. The amount of dirt removed (difference between starting
weight and ending weight after the load is washed and dried) is the response. The data are given
below.
Treatment
1
2
3
4
Detergent
Brand
X
Y
X
Y
Water
Temp
Warm
Warm
Hot
Hot
Amount of Dirt (g)
Removed
13 16 16 14 17
17 19 20 17 20
18 16 17 19 20
21 20 18 22 23
Mean
15.2
18.6
18.0
20.8
Variance
2.7
2.3
2.5
3.7
(a) Is this a well designed experiment? Comment briefly on control of outside variables, randomization
and replication.
(b) Calculate means for each treatment combination, Detergent Brand and Water Temperature.
(c) Display the means for Detergent Brand and Water Temperature graphically and comment on the
apparent effects of each factor.
(d) Construct two interaction plots, one with Detergent Brand on the horizontal axis, one with Water
Temperature. Does there appear to be an interaction between the two factors?
(e) Compute the M SrepError by pooling the individual sample variances for each treatment combination.
(f) Calculate the estimated full effect for each factor and the interaction effect.
(g) Give the standard error of an estimated full effect and use it to determine what estimated effects
are statistically significant. Use t=3 for the critical value.
(h) Eliminate any nonsignificant effects and give the reduced model prediction equation. Be sure to
define the coded predictors explicitly.
(i) Predict the values for the four treatment combinations. Construct prediction intervals for each of
these values.
(j) What recommendation would you make to get the most dirt out?
(k) We could also look at this as a “one-factor” experiment, where the “treatments” for the “onefactor” are combinations of detergent and water temperature. Calculate the LSD (use t=2) for
such an experiment.
(l) Based on the LSD, which “treatments” are significantly different? not significantly different?
Based on this analysis which combination of detergent brand and water temperature would you
recommend?
Note: You may use JMP, or another computer program, to assist you with any of the graphing or calculations
needed to answer the questions above. However, since exams will contain some hand calculations it may be
worthwhile to do the calculations by hand and verify the hand calculations with the computer.
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