Stat 411 Discussion Week 10
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
I. Definition
1. One-stage sampling with replacement
For total
Mi
i = P(unit i is selected on first draw) = M
0
P
P
ti
1
t = n1
=
u
=
u
,
where
u
is
an
un
Stat 411 Discussion Week 2
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
I. Definition
1. Simple random sampling from a finite population, and estimate the population mean yU , the estimator is
P
2
n
n
yS = n1 iS yi . The varian
Stat 411 Discussion Week 8
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
I. Definition
1. Regression
P Estimation y = B0 + B1 x
(xi x
)(yi y)
rsy
1 = iS
P
B
=
2
(x
x
)
sx
iS i
B0 = y B1 x
0 + B
1 x
1 (
y
reg = B
U = y + B
xU x
)
Stat 411 Discussion Week 12
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
I. Definition
1. Unequal-probability one-stage sampling without replacement
i = P(unit i in sample)
ij = P(units
i and k are both in the sample)
P
tHT 1 =
Stat 411 Discussion Week 6
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
I. Definition
1. Ratio Estimation in SRS
= y = ty
B
x
tx
x
tyr = Bt
x
y
r = B
U
2. Ratio Estimation in SRS is biased
x
Bias(y
r ) = -Cov(B,
)
3. residua
Stat 411 Discussion Week 1
Shizhen Wang [email protected]
I. Definition
1. Review of probability
Elementary outcome is an event which contains only a single outcome in the sample space.
Sample space () is the list of all possible outcomes.
Event is a
Stat 411 Discussion Week 4
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
1. A typical opinion poll surveys about 1000 adults. Suppose that the sampling frame contains 100 million adults including
yourself, and that an SRS of 100
Stat 411 Discussion Week 3
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
I. Definition
1. For simple random sampling without replacement
PN
2
n
Var(
yS ) = Sn (1 N
), where S 2 = N 11 i=1 (yi yU )2
2
n
Var(tS ) = N 2 Sn (1 N
)
p
Stat 411 Discussion Week 9
Shizhen Wang [email protected] MSC 1275
OH Mon 11-12 Tue 3-4 Fri 1-2
I. Definition
1. One-stageP
cluster sampling with unequal sizes - unbiased estimator
tunb = N
iS ti
n q
s2
n
se(tunb ) = (1 N
)N 2 nt , where s2t is the sa