Let U be a population of size N. From U, we first select a SRSWOR, 1 S , of size 1 n . Then, from 1 S , we select a SRSWOR, 2 S , of size 2 n .
statistics
Description
1. (10 marks) Let U be a population of size N. From U, we first select a SRSWOR, 1 S , of size 1 n . Then, from 1 S , we select a SRSWOR, 2 S , of size 2 n . Show that 2 S is a SRSWOR of size 2 n selected from U
2. (20 marks) Let U be a population of size N. From U, we first select a SRSWOR,
1 S
, of size
1 n
. Then, from
U
\
1 S
, we select a SRSWOR,
2 S
, of size
2 n
. The final sample is
1 2 S S S =
of size
1 2 n n n = +
. Let
1
1
1
1
k
k S
y y
n
=
and
2
2
2
1
.
(a) (5 marks) Show that S is a SRSWOR of size n selected from U. What is interesting
about this result?
(b) (10 marks) Show that
( )
2
2
2
2
1 , y
p
n S
V y
N n
= −
where
( )
2
2 1
1
y k
k U
S y Y
N
= −
−
with
1
.
k
k U
Y y
N
=
Hint: You may want to show first that
2 S
is a SRSWOR from U.
3. (15 marks) The files Parishes_pop shows data on a population of parishes in Quebec. The file
Parishes_sample shows data from a SRSWOR of size 50 selected from the population.
Instruction Files
Assignment1sampling.pdf
154.7 KB
