STAT 854/454
Short Solutions to Assignment 4
1. Let ty = N yi be the population total. Consider linear estimators of ty in the form i=1 ^ of tL = is wi yi , where s is the set of sampled units and wi is a constant to be used as a weight for the ith elemen
STAT 854/454 Sampling Theory and Practice
Due: Wednesday, March 11, in class
Assignment 4
Format: standard A4 size paper, single-sided, with a cover page 1. Let ty = N yi be the population total. Consider linear estimators of ty in the form i=1 ^ of tL =
STAT 854/454 Sampling Theory and Practice
Due: Wednesday, February 25, in class
Assignment 3
Format: standard A4 size paper, single-sided, with a cover page 1. An accounting firm is interested in estimating the error rate in a compliance audit it is condu
STAT 854/454 Sampling Theory and Practice
Due: Wednesday, January 21, in class
Assignment 1
Format: standard A4 size paper, single-sided, with a cover page 1. For each of the following surveys, describe the target population, sampled population, sampling
STAT 454/854
Short Solutions to Assignment 1
1. For each of the following surveys, describe the target population, sampled population, sampling frame, response variable(s) and population quantities of interest. Discuss specific structures of the populatio
STAT 854/454
Short Solutions ro Assignment 3
1. An accounting firm is interested in estimating the error rate in a compliance audit it is conducting. The population contains 828 claims, and each claim consists of 215 fields. The firm audits 85 claims sele
STAT 854/454
Short Solutions to Assignment 5
1. Suppose the finite population follows the model (): yi = xi + i , i = 1, 2, , N , where xi > 0 and the i 's are independent random variables with E (i ) = 0 and V (i ) = xi 2 . The finite population mean x f
Metrika, Volume 27, 1980, page 277-279. 9 Physica-Verlag, Vienna.
A N ote on the Comparison Between Simple Random Sampling
w ith and without Replacement
B y M.N. Deshpande, A urangabad I )
Summary: A new approach is suggested for comparing SRSWR and SRSWO
STAT 854/454
Sampling Theory and Practice
(For Practice Only, Do Not Hand-In!)
Assignment 5
1. Suppose the finite population follows the model (): yi = xi + i , i = 1, 2, , N , where xi > 0 and the i 's are independent random variables with E (i ) = 0 and
STAT 854/454
Short Solutions to Assignment 2
1. Let N = 7, 800 be the number of public schools in Canada. We wish to estimate p = M/N , where M is the number of schools that have Wireless Internet Access (WIA). (a) Find the required sample size n such tha
STAT 454/854
Instructions for the Final Project (Winter 2012)
1. Project Requirements
Individual project with topics approved by the instructor
Word or LaTeX processed nal report with minimum eight double-spaced pages (including tables, graphs, acknowle
STAT 854/454 Sampling Theory and Practice
Due: Wednesday, February 4, in class
Assignment 2
Format: standard A4 size paper, single-sided, with a cover page 1. Let N = 7, 800 be the number of public schools in Canada. We wish to estimate p = M/N , where M
STAT 854/454 Sampling Theory and Practice
Due: Tuesday, February 8, in class
Assignment 2
Format: standard letter size paper, single-sided, with a cover page 1. Consider a stratied population with H = 3, N1 = 500, N2 = 1000, N3 = 1500. Suppose 2 2 2 that
STAT 454/854
A Sample R Program for Simulation Studies
Winter 2009
1. Objectives: To evaluate finite sample performances of y and p and the related normal ^ theory confidence intervals on the population mean y and the population proportion p under SRSWOR.
STAT 854/454
Sampling Theory and Practice
Assignment 4
Due: Tuesday, March 13, 2012, in class
1. Suppose the nite population follows the model ( ): yi = xi + i , i = 1, 2, , N , where
xi > 0 and the i s are independent random variables with E (i ) = 0 and
STAT 330
EXTRA PROBLEMS CHAPTERS 1 TO 4
1. Consider the following functions:
(a) f (x) = kx(0.3)x ,
x = 1, 2, 3, .
2 1
(b) f (x) = k (1 + x )
|x|
(c) f (x) = ke
,
(e) f (x) = kx
< x <
< x <
2 x
(d) f (x) = kx e
,
,
( +1)
,
x > 0, > 0
x > > 0, > 0
In e
STAT 454/854
Winter 2012
Handout #1
Basic Results Under SRSWOR
(1) Point estimation: y is unbiased estimator of y , i.e., E () = y .
y
(2) The theoretical variance formula:
V () = 1
y
2
n y
,
Nn
where n/N = f is the sampling fraction and 1 f is called th
STAT 454/854
Winter 2012
Handout #2
Single-stage Cluster Sampling
(1) Single-stage cluster sampling with clusters of equal sizes
We have Mi = M , i = 1, , N and K = N M . The population mean is y =
N 1 N i , where i = M 1 M yij . Under single-stage cluste
STAT 854/454
Short Solutions to Assignment 4
1. Suppose the nite population follows the model ( ): yi = xi + i , i = 1, 2, , N , where
xi > 0 and the i s are independent random variables with E (i ) = 0 and V (i ) = xi 2 .
The nite population mean x for t
STAT 454/854
Winter 2012
Handout #3
Unequal Probability Sampling and the HT Estimator
Let i and ij be respectively the rst order and the second order inclusion probabilities
under a general sampling design. The Horvitz-Thompson (HT) estimator for the popu
STAT 454/854
Winter 2012
Handout #5
PPS Sampling With Replacement
Let x1 , x2 , , xN be the values of a size variable x. Let zi = xi /tx : zi > 0 and N zi = 1.
i=1
Under PPS sampling with replacement, the rst unit is selected from cfw_1, 2, , N with
prob
STAT 454/854
Short Solutions to Assignment 2
1. Consider a stratied population with H = 3, N1 = 500, N2 = 1000, N3 = 1500. Suppose
2
2
2
that we know the stratum population variance y1 = 100, y2 = 200, y3 = 225. We like to
take a stratied simple random sa
STAT 854/454
Short Solutions to Assignment 3
1. Let ty = N yi be the population total. Consider linear estimators of ty in the form
i=1
of tL = is wi yi , where s is the set of sampled units and wi is a constant to be used as a
weight for the ith element
STAT 854/454 Sampling Theory and Practice
Assignment 3
Due: Tuesday, February 28, 2012, in class
1. Let ty = N yi be the population total. Consider linear estimators of ty in the form of
i=1
tL = is wi yi , where s is the set of sampled units and wi is a
STAT 454/854
Winter 2009
Handout #5
Brewer's PPS Sampling Method for n = 2
Suppose that 0 < zi < 1/2 for all i and
N i=1 zi
= 1.
1. Draw the first element with probability equal to pi = zi (1 - zi )/cfw_D(1 - 2zi ), i = 1, , N , where D is a constant sati
STAT 454/854
Winter 2009
Handout #4
Unequal Probability Sampling and the HT Estimator
Let i and ij be respectively the first order and the second order inclusion probabilities under a general sampling design. The Horvitz-Thompson (HT) estimator for the po
STAT 454/854
Winter 2009
Handout #3
Single-stage Cluster Sampling
(1) Single-stage cluster sampling with clusters of equal sizes We have Mi = M , i = 1, , N and K = N M . The population mean is y = N -1 N i , where i = M -1 M yij . Under single-stage clus
STAT 454/854
Winter 2009
Handout #2
Sample Size Calculation Under SRSWOR
(1) Precision specified by P (| - y | < e) = 1 - y . n=
2 2 z/2 y 2 2 e2 + z/2 y /N
(2) Precision specified by P (| - y |/y < e) = 1 - y . n=
2 2 z/2 y 2 2 e2 2 + z/2 y /N y
(3) Samp
STAT 454/854
Winter 2009
Handout #1
Some Commonly Used Terms
1. Target population: The complete collection of individuals or elements we intend to study, defined by the main objective of the study. 2. Sampling frame: The complete list of sampling units fr
STAT 854/454 Sampling Theory and Practice
Assignment 1
Due: Thursday, January 19, in class
Format: standard A4 or letter size paper, single-sided, with a cover page
1. For each of the following surveys, describe very briey the target population, the sampl