Chapler7. Ln?)
BILL WELBOURN
HOMEWORK SET#2 — CHAPTER7 : PROBLEM#17, 18, 19 ab
DUE DATE — JUNE 8, 2004
CHAPTER 7
(17) Considerthe standard normal distribution with mean ,u = 0 and variance 02 = 1.
Questions: (a) What is the probability that an outcome 2
524
Chapter 15
Table 15.40
Fractional Factorial Experiments
Output from SAS program for the sludge experimentve-way model, with too
many terms
The SAS System
General Linear Models Procedure
Dependent Variable: Y
Source
A
B
C
D
E
A*C
B*C
B*D
DF
1
1
1
1
1
1
15.8
Table 15.41
Using SAS Software
525
SAS program for the product array analysis of the inclinometer experiment.
DATA INCLP;
INPUT A B C D E F G Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8;
SUM = (Y1 + Y2 + Y3 + Y4 + Y5 + Y6 + Y7 + Y8);
AVY = SUM/8;
VAR = (Y1*Y1 + Y2*Y2 +
15.8
Table 15.39
523
Using SAS Software
Output from the SAS program for the sludge experimentve-way model
The SAS System
General Linear Models Procedure
Dependent Variable: Y
Source
DF
Type III SS Mean Square F Value
A
1
861.1
861.1
.
B
1
78606.1
78606.1
15.8
Figure 15.7
Plots of the effect of
the levels of factor D
for the inclinometer
experiment, where
xijklmnp denotes
average response and
vijklmnp denotes the log
sample variance ln(s 2 )
for corresponding
design factor
combinations
Table 15.36
521
Usin
520
Chapter 15
Table 15.34
Fractional Factorial Experiments
Analysis of variance for average response for the inclinometer
experiment
Source of
Variation
A
Linear A
Quadratic A
B
Linear B
Quadratic B
C
Linear C
Quadratic C
D
Linear D
Quadratic D
E
Linear
522
Chapter 15
Table 15.37
Fractional Factorial Experiments
Output from SAS program for the sludge experimentcell-means model
The SAS System
General Linear Models Procedure
Dependent Variable: Y
Sum of
Mean
Source
DF
Squares
Square F Value
Model
7
1510451
15.7
Table 15.32
Analysis of variance for ln(s 2 ) response for the inclinometer
experiment
Source of
Variation
A
Linear A
Quadratic A
B
Linear B
Quadratic B
C
Linear C
Quadratic C
D
Linear D
Quadratic D
E
Linear E
Quadratic E
F
Linear F
Quadratic F
G
Err
518
Chapter 15
Table 15.31
Fractional Factorial Experiments
Maximum angle of swing for the inclinometer experiment. Combinations
of design factors AG are in rows, and combinations of noise factors HN
are in columns.
H
P
Noise J
Factors: K
L
M
N
Design Fac
516
Chapter 15
Fractional Factorial Experiments
experiment is to nd out which factors most affect the log variance response, and which
factors most affect the average response. Design combinations are then sought that give a
low sample variance across the
15.7
Design for the Control of Noise Variability
517
D: Flange thickness (1.0, 3.5, 6.0)
E: Flange width (6.0, 10.5, 15.0)
F : Bob-weight length (12.0, 20.0, 28.0)
G: Copper plating thickness (0.0175, 0.035, 0.07)
All measurements are in millimeters, and
15.8
Table 15.43
527
Using SAS Software
Output from the SAS program for the inclinometer experimentmixed-array
analysis
The SAS System
General Linear Models Procedure
Dependent Variable: Y
Sum of
Mean
Source
DF
Squares
Square F Value
Model
119
1245.7533
1
Exercises
529
evidence to conclude that factor B (exure thickness) affects the swing signicantly, it may
still be of interest to examine the direction of any trend that may be present (the p-value for
the test of no effect of factor B is 0.019). The least
Initials:
Biostatistics 200
Fall 2012 Exam 1 Review Question Solutions
Tuesday, 1 November 2012
The best way to study for a Biostatistics 200 exam is to work problems; the problems
contained in this review should be helpful in your preparation for exam 1.
1
Chapter 3: Conditional Probability and Independence
3.1. Conditional Probability
As we saw in Chapter 2, when conducting an experiment, we are often interested in the
probabilities of two or more events. At times, some partial information about the
outc
International Graduate School of Genetic and Molecular
Epidemiology (GAME)
Classroom exercises
Paul W. Dickman
September 2003
Contents
1 Probability
2
2 Binomial distribution
5
3 Normal distribution
9
4 Sampling/study design
12
5 One-sample inference for
Probability and Conditional Probability
Department of Statistics
University of WisconsinMadison
Probability
1 / 30
Readings
3.13.3
Probability
2 / 30
Parasitic Fish
Case Study
Consider an experiment in which sh are placed in a large tank for a
period of t
9/6/01
Probability
"
Descriptive statistics used to summarize a set of
data
"
Goal: Make inferences about a population based
on data contained in a sample from the population
"
Statistical Inference is built on a foundation based
on Probability Theory
Bas
CHAPTER 6
Exercise 7
a. An B is the event that the individual is exposed to high levels of both carbon monoxide and
nitrogen dioxide.
b. Au B is the event that the individual is exposed to either carbon monoxide or nitrogen
dioxide or both.
c. AC is the e
Chapter 7. 1-6, 8-10
Solutions
7-1. What is a probability distribution? What forms may a probability distribution take?
Solution: A probability distribution is a set of values with associated probabilities where the
values are mutually exclusive, and the
533
Exercises
main effect of F was selected as one of the contrasts for confounding. All the 2-factor
interactions and most of the 3-factor interactions were thought to be of interest. Unlikely
3-factor interactions included ACG and BDE, which were also c
514
Chapter 15
Fractional Factorial Experiments
factor, is aliased with C, and the dening relation is
I
ABD1
ABCD2
CD1 D2 .
This is a Resolution II design, which should be avoided if possible, since it confounds two
main effects (C and D). A better design
512
Chapter 15
Table 15.27
Fractional Factorial Experiments
Contrast estimates for log sample variance response variable
Contrast
Estimate
Table 15.28
A
0.352
B
0.122
C
0.105
D
0.249
E
0.012
F
0.072
G
0.101
H
0.566
F
0.060
G
0.098
H
0.142
Contrast estimat