STAT 496, Spring 2013
Homework Assignment #3, Due by Friday, February 15
1. An important quality characteristic in the manufacture of pulp used in paper is the pulp
brightness. Pulp brightness is measured with a reflectance meter. Each of four shift operators
makes five pulp hand-sheets from unbleached pulp. Reflectance is measured for each of the
hand-sheets using the reflectance meter. Each operator measures the hand-sheets she/he has
made. The data are given below and the JMP analysis appears at the end of this homework
assignment.
Mean, Yi
Variance, si2
O1
60.3
60.0
60.1
60.2
59.8
60.08
Operator
O2
O3
59.8
60.7
60.2
60.7
60.4
60.5
59.9
60.9
60.0
60.3
60.06
60.62
O4
61.0
60.8
60.6
60.5
60.5
60.68
0.037
0.058
0.047
0.052
a) Explain briefly why this is an observational study?
61
Reflectance
61
60
60
59O1
O2
O3
O4
Operator
b) Comment on the plot of the data. Be sure to discuss both center and spread.
c) Calculate, by hand, the value for the Least Significant Difference (LSD) using t=3.
Indicate which pairs of operators have differences in mean reflectance that are
statistically significant.
d) How does your analysis in c) compare to JMP using Comparisons - Each pair, Student's t
and an individual error rate of α = 0.01?
Because each operator measured the hand-sheets that she/he had made, we can’t be sure if
differences in mean reflectance are due to how the operators make the hand-sheets or how
they measure the hand-sheets.
e) If we were interested in looking at differences due to the way the operators make the
hand-sheets, how would you change the data collection to investigate this?
f) If we were interested in looking at differences due to the way the operators measure the
hand-sheets, how would you change the data collection to investigate this?
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2. A manufacturer of videotape runs an experiment to investigate the relationship between the
video tape manufacturing line speed and the number of flaws in an 800 meter roll of
videotape. There are four line speeds (10, 20, 30 and 40 decimeters per second). Only one
manufacturing line is used in the experiment. There is one operator for the line. All the raw
material comes from the same batch. The flaws on each video tape will be counted by the
quality engineer using a detailed operational definition of what a flaw is. Six video tapes are
manufactured for each line speed. The order of the 24 runs (rolls of videotape) will be
completely randomized. The data are given on the next page.
10
10
5
12
8
14
8
9.5
10.3
Y
s2
Line Speed (dcm/sec)
20
30
14
13
12
18
16
10
13
13
9
15
8
18
12.0
14.5
9.2
9.9
40
17
16
12
15
22
14
16.0
11.6
a) Comment on the control of outside variables, randomization and replication within the
experiment. Be specific.
25
Number of
Tape Flaws
20
15
10
5
0
0
10
20
30
40
50
Line Speed
b) Comment on the general trend in the plot of tape flaws versus line speed.
c) Code the line speed using the formula below. Calculate the simple linear regression line
relating density to coded line speed.
 Line Speed - 25 
C 1i = 2

10


d) Reverse the coding for your equation in c) to obtain the simple linear regression relating
number of tape flaws to line speed. Graph this line on your plot in a).
e) Predict the number of tape flaws for a line speed of 35.
f) What percentage of the variability in the number of tape flaws is explained by the linear
regression with line speed? Note: SSTotal=352.0.
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g) Is there a significant linear relationship between the number of tape flaws and line speed?
How do you know? Caution: Be sure to use MSRepError
h) Add a quadratic term to you prediction equation by using the coded variable:
 C
C 2i =   1i
 2

i)
j)
2
15 

 − 
12 


What percentage of variability in the number of tape flaws can be explained by the
addition of this quadratic term?
Is the quadratic term statistically significant? How do you know? Caution: Be sure to
use MSRepError
Oneway Anova for the Reflectance of Pulp Hand-sheets Study
Summary of Fit
Rsquare
Adj Rsquare
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
Analysis of Variance
Source
DF
Operator
3
Error
16
C. Total
19
0.685575
0.626621
0.220227
60.36
20
Sum of Squares
1.6920000
0.7760000
2.4680000
Mean Square
0.564000
0.048500
F Ratio
11.6289
Prob > F
0.0003*
Means Comparisons
Comparisons for each pair using Student's t
t
Alpha
LSD
2.92078
0.01
0.40682
Abs(Dif)-LSD
O4
O3
O1
O2
O4
-0.40682
-0.34682
0.193182
0.213182
O3
-0.34682
-0.40682
0.133182
0.153182
O1
0.193182
0.133182
-0.40682
-0.38682
O2
0.213182
0.153182
-0.38682
-0.40682
Positive values show pairs of means that are significantly different.
Level
O4
O3
O1
O2
A
A
B
B
Mean
60.680000
60.620000
60.080000
60.060000
Levels not connected by same letter are significantly different.
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