Homework 4
Review Sections 3.1, 3.2, 3.3, 3.4, 3.5; my notes, Chap 3, Parts 1 to 3 and Lab 5.
Practice problems: 3.1, 3.2, 3.3
Problems for submission:
Problem 1
Suppose that you are planning to run an experiment with one treatment factor having five
leve
Stat 470 Fall 2013
Homework 6
Review Sections 4.1; my notes, Chap 4, slides 1- 28 and Lab 7.
Problem 1. Q3.4, 4.2
Q 3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the Pvalue.
Source
Factor
Error
Total
DF
?
25
29
SS
Lady Tasting Tea1
R. A. Fisher was one of the founding fathers of modern statistics. One of his early, and perhaps
the most famous, experiments was to test an English ladys claim that she could tell whether milk
was poured before tea or not. Heres an acco
Stat 470 Fall 2016
Homework 6 Solution
Problem 1. Q3.49
a) Normal equations are given by minimizing
3
=
3
5
3
2
=1 =1
5
. = 0
=1
3
2
min ( )
. = 0
=1 =1
=1
So the nor mal equations are given as
1.
= 2 3=1 5=1( ) = 0
2(3=1 5=1 15 3=1 ) = 0
2(3=1 5=1 1
Stat 470 Fall 2016
Homework 9 Solutions
Problem 1. 6.1. An engineer is interested in the effects of cutting speed (A), tool geometry (B),
and cutting angle on the life (in hours) of a machine tool. A certain design was run and the
results are
Homework 8 solutions
Stat 470, Fall 2016
Problem 1. Consider Problem (Q5.9) you did in homework 7. Draw the response surface for
thrust using the code you learned in Lab 10. Use the following regression model and code:
2
2
= 0 + 1 1 + 2 2 + 3 1 2 + 4 1
+
Stat 470 HW 7 Solution
Solution to Problem 1, Q 5.9:
(1) The boxplots in Figure 1 show that there are differences across treatment levels of Drill
Speed and of Feed Rate. The spread varies across the different levels of Drill Speed but less so
across the
Stat 470 HW 1 Solution
Problem 1: Refer to the lady tasting tea experiment. Read the two articles
posted on CTools. Then answer the following questions: (1) Suppose Miss Bristol
was able to identify 6 out the 8 cups correctly. If the desired significance
Stat 470 HW 2 Solution
2.25
We assume the breaking strength of two types of plastic are both normal. Our hypotheses
1 y2 10
are: H0 : 1 2 = 10; H1 : 1 2 > 10 Test statistic: Z0 = yr
= 5.8387
2
2
1
+ n2
n1
2
Using N(0; 1) distribution, the p-value is: P (Z
Stat 470 Fall 2016 HW 5 Solution
3.26
(a)Our hypotheses are: H0 : 1 = 2 = 3 vs. H1 : At least one i is different from another.
Our test statistic is: F = 38.34 F2,12 .
Our p-value is: 6.141 106 .
Our decision is: Reject H0 because 6.141 106 < = .05.
Our c
Stat 470 HW4 Solution
1.
(i) The standardized residual plot in Figure (1) shows some large residual values that might
indicate presence of outliers. The normal probability plot (Figure 1) shows that the assumption
of normality is reasonable except for the
A Laboratory Guide for
Stat 470: Introduction to Design of Experiments
LAB 2: Population distributions and sampling distributions
Objective:
a) To understand the difference between a population distribution and a sampling
distribution; and
b) The effect o
Stat 470 Fall 2013
Designing an experiment
Aspects of an Experimental Design
Objective of study, critical in setting up an appropriate design and
all its aspects.
Response variable, what are we going to use to achieve our
objective of study?
Factors and l
Stat 470 Fall 2012
Chap 2 Part 1
Review of analysis for a single sample
Review of analysis for a single sample
A review of statistical concepts for a single sample
Looking at data
Review of sampling and sampling distributions
Inference: estimation, confid
Stat 470
Introduction
What we will do today
An introduction to us
Introduction to the course and its
management
About R and Stat 470
Why take a course on experimental
design?
An introduction to us
You and me
My name: Shyamala Nagaraj
You and your GSI
Stat
Part 1: Experiments with a single factor: two examples
(Sec 3.1)
Part 2: Analysis of variance (Secs 3.2, 3.3)
Part 3: Diagnostics and interpretation (Secs 3.4, 3.5)
Part 4: Least squares and ANOVA (Secs 3.3, 3.10)
Part 5: Sample size and power (Sec 3.7)
Review of analysis for two samples
Sample size determination
The diameter of a ball-bearing was
measured using two different types of
calipers
> y1
[1] 0.265 0.265 0.266 0.267 0.267 0.265 0.267
0.267 0.265 0.268 0.268 0.265
> y2
[1] 0.264 0.265 0.264 0.26
Stat 470
Fall 2012
Chap 2 Part 3
Models for one and two samples: Least squares Estimation
These notes deal with estimation of the parameters of a model by least
squares. The relationship between the res
Design of experiments with a single factor: two
examples (Sec 3.1)
Model and es=ma=on (Secs 3.2, 3.3)
ANOVA, diagnos=cs and interpreta=on (Secs 3.4, 3.5)
Sample size and power (Sec 3.7)
A real applica=on (Sec 3
A Laboratory Guide for
Stat 470: Introduction to Design of Experiments
LAB 1: introduction to R and the decomposition of the sums of squares
Purpose of Lab 1: Introduction to R and the summation sign. This lab guide provides
a brief note on R and examples
STAT 470: Introduction to the Design of Experiments
FALL 2013
Instructor:
Dr. Shyamala Nagaraj
270 West Hall, 734-764-5493, [email protected]
GSIs: Pramita Bagchi, [email protected],
Nirupam Chakrabarty, [email protected]
Calendar Commitments:
Lectures:
Stat 470 Fall 2016
Homework 1
Problem 1
Refer to the lady tasting tea experiment. Read the two articles posted on Canvas. Then answer
the following questions:
(1) Suppose Miss Bristol was able to identify 6 out the 8 cups correctl