Chapter 7 Exercise Solutions 1. Consider the sampling protocols defined in Example 1. a) Show that the inclusion probability for each unit in the frame is 1/100 for every protocol. For each protocol, the model is uniform. That is, the chance of any p
Chapter 5 Exercise Solutions 1. A large organization is planning a massive retraining of its employees in the use of Office programs. As part of the planning, the HR department considers two factors that might impact the success of the training Facto
Stat 322/332 Sampling and Experimental Design
Assignment 2
Due: Wednesday, October 8, 2008 (12:30pm in class)
1. Consider the model for the balanced completely randomized design.
Yij = + i + Rij , Rij G(0, ), i = 1, . . . , t, j = 1, . . . , r
Where i i =
Stat 322/332 Sampling and Experimental Design:
Assignment 4
Due: Wednesday, Nov. 12, 2008, 12:30-1:20
1. For each of following surveys, describe briey 1) the target population; 2) population
structure and sampling frame; 3) the study population; 4) the re
Chapter 9 Exercises Solutions 1. In many surveys, there is interest in estimating strata averages or differences in strata averages. ~ ~ ~ a) In general, for SRS, write down the distribution for the estimators h and h - k .
Assuming relatively lar
Stat 322/332 Experimental Design and Sampling
Midterm
Monday, October 27, 2008, 3:30-4:30
An experiment was conducted to investigate the eectiveness of a new fungicide for grape
plants. Part of a vineyard was divided into three blocks, and four treatments
Stat-332 Short Solutions to Assignment 2
1. Look at the solution of Question 4 in the exercises of Chapter 3 in your course notes. 2. (1) s2 = 0.500 and s2 = 0.125. 3 4 (2) Model Yij = +i +Rij , i = 1, . . . , 4 and j = 1, 2 with Rij G(0, ) and the
1
University of Waterloo
STAT 332
Sampling and Experimental Design
Course Notes
Winter 2016
by
JOCK MACKAY
[email protected]
STEFAN STEINER
[email protected]
MATTHIAS SCHONLAU
[email protected]
2
The material in these notes is derived and com
Stat 332 - Assignment 03 (Due Friday June 27, 4:00 PM)
Remarks:
You may use any software that you like to perform your computations.
You may include output from your software in your solutions to show how you are obtaining
your results.
You must show y
Stat 332 - Assignment 01 - Solutions
[10]
1. In an Ontario study, 50267 live births were classied according to the babys weight (less
than or greater than 2.5 kg.) and according to the mothers smoking habits (non-smoker,
1 20 cigarettes per day, or more t
Stat 332 - Assignment 05 (Due Wednesday July 30, 4:00 PM)
Remarks:
You may use any software that you like to perform your computations.
You may include output from your software in your solutions to show how you are obtaining
your results.
You must sho
Stat 332 - Assignment 02 - Solutions
Remarks:
You may use any software that you like to perform your computations.
You may include output from your software in your solutions to show how you are obtaining
your results.
You must show your setup clearly,
Homework Wed., May 29, 2013
1. Show that for the model Yi=+Ri where Ri N(0,2), and i=1,2,n; W=iri =0.
2. Show that for models 1, 2 and 3, our MLE estimates correspond to the OLS estimates.
3. Consider the model Yij= +i+Rij where Rij N(0,2), and j=1,2,n an
STAT 322 Homework 3
1. For the model Yij=i+Rij where Rij N(0,2), and j=1,2,n and i=1,2;
a. Show the estimates i are the sample means.
b. Show that
2. A researcher wanted to find the effect of a special diet on blood pressure. She selected
a sample of 5 ad
Homework 9
Hint: These questions are all about indicator variables.
Question 1:
The inhabitants of the beautiful and ancient canal city of Pentapolis live on 5 islands separated from each
other by water. Bridges cross from one island to another as shown.
Homework Wed., May 15, 2013
1. For the model Yij=i+Rij where Rij N(0,2), and j=1,2,n and i=1,2; determine the distribution of
~ ~ .
1 2
2. A researcher wanted to find the effect of a special diet on blood pressure. She selected a
sample of 5 adults and pu
Homework Wed., May 22, 2013
1. A researcher wanted to find the effect of a special diet on blood pressure. She selected a
sample of 5 adults and put them on this plan for a year. At the start and end of the year she
measured their blood pressure. The resu
STAT 322 Homework 4
1. For the model Yij= +i+Rij where Rij N(0,2), and j=1,2,r and i=1,2;
a. How many units have you investigated?
+
i+
y
y
b. Show the estimates of and i using OLS are respectively + , .
y
c. Show that the estimate of 2 in this case is s
Homework July 3, 2013
Hint: These questions are all about indicator variables.
Question1:
TheinhabitantsofthebeautifulandancientcanalcityofPentapolisliveon5islandsseparatedfromeachotherby
water.Bridgescrossfromoneislandtoanotherasshown.
Onanyday,abridgeca
Homework June 12, 2013
1.
Consider the model Yij= +i+Rij where Rij N(0,2), and j=1,2,r and i=1,2,t. Show that,
a.
r (Y
i
E(
b.
Y ) 2
i
t 1
( yij y )2
i, j
=
) 2 r
i
t 1
( yij yi )2
i, j
2
i
+
r( y
i
i
y ) 2
STAT 322 Homework 1
Question 1: Answer the following with either TRUE or FALSE. A clear answer is required. Please assume
that your answer to a 90% confidence interval for was (A,B).
a) With 90% probability we can be certain that
b) The confidence interva
Experimental plans for more than 2
treatments: ANOVA and sample size
Kun Liang
2014 Fall
F distribuBon
R code
> anova(b)
Analysis of Variance Table
Response: energy
Df Sum Sq
Factorial Treatment Structure
and Interaction: part 2
Kun Liang
2014 Fall
Example: Longevity of Roses
Commercial flower grower sells cut roses
Grower wants the roses to last as long as
possible
Investigate two different ways of cutting the
stems, and t
Experimental plans for more
than 2 treatments: contrast
Kun Liang
2014 Fall
Overview
Intro to Data sets
Model and Analysis (balanced)
Contrasts
Motivation
Previously, we had 2 treatments (2 groups)
Now we consider plans with more than 2
treatments
De
Experimental Design:
Two treatments
Kun Liang
2014 Fall
Single factor
[email protected]: whether the treatments have
dierent eects
Assume response variable y is [email protected]
We will start with two treatments
General setup