Math/Stat 423/523 Exam 2
Spring 2006
Solution Key
1.
An experiment was carried out to study the effects of factors A, B and C. ANOVA table and interaction plot are given below. Source A B C A*B A*C B*C A*B*C Error Total DF 1 2 2 SS 17.36 MS 17.36
SAS Output Example 1A
The SAS System
15:31 Monday, February 2, 2015 1
The GLM Procedure
Class Level Information
Class
Levels
NADP
4
Values
1234
Number of Observations Read
Number of Observations Used
The SAS System
20
20
15:31 Monday, February 2, 2015 2
T
Math/Stat 423/523
Example #2
A textile mill has a large number of looms. Each loom is supposed to provide the same
output of cloth per minute. To investigate this assumption, five looms are chosen at
random, and their output is measured at four different
Math/Stat 423/523
Spring 2016
Assignment #1
Due: Tuesday, February 2, 2016
Instructions: In doing problems of tests of hypotheses below, you must first find the Pvalue and then make your decisions based on the Pvalue.
Please write your answers only on on
SAS Output Example 1B
The GLM Procedure
Class Level Information
Class
Levels
NADP
4
Values
1234
Number of Observations Read
Number of Observations Used
20
20
The GLM Procedure
Dependent Variable: SPAC
Source
DF
Sum of
Squares
Model
3
14.52545500
4.8418183
Math/Stat 423/523
Example #1
The mitochondrial enzyme NAPH:NAD of the common rat tapeworm (Hymenolegsis
diminuta) catalyzes hydrogen in transfer from NADPH to NAD, producing NADP. This
enzyme is known to serve a vital role in the tapeworms anaerobic metab
Assignment #2
Due: Tuesday, February 18, 2016
1. An article in the ACI Materials Journal describes several experiments investigating
the rodding of concrete to remove entrapped air. A 3 6 cylinder was used, and
the number of times this rod was used is the
Math/Stat 423/523 Section 10.1
Chapter 10
Formulas
SingleFactor ANOVA (Equal Sample Sizes)
I = total number of treatments J = common number of replications of each treatment mean of treatment i (for i = 1, 2, ., I) i = Xij = random variable that
Math/Stat 423/523 Section 11.1
Chapter 11 Formulas Set
TwoFactor ANOVA with No Replications
Notation A = 1st factor, I = number of levels of A B = 2nd factor, J = number of levels of B Xij = the measurement from the combination of the i th level
Math/Stat 423/523 Chapter 12 Formulas
Linear Model: Yi = β0 + β1xi + εi where ε's are iid N(mean=0,variance=σ2).
•
β1 = average change in Y for every unit change in x
•
µy•x* = β0 + β1x* = average response at x*
•
σ2y•x* = variance of Y at x=x*
A

∑ xiyi
Math/Stat 423/523 Chapter 13 Formulas Section 13.1 i
th
More on Residuals
residual (random version) is Ei
Yi
xi
^ Yi
x Sxx
2
E Ei
0, V Ei
2
1
1 n
Ei ~ N mean (
where Sxx
0, variance
2
V Ei
xi
x
Standardized residual
e* i s 1
yi 1 n
Math/Stat 423/523
Example #7
An engineer is interested in the effect of cutting speed (A), metal hardness (B), and
cutting angle (C) on the life of a cutting tool. Two levels of each factor are chosen, and
two replicates of a 23 factorial design are run.