Download Powerpoint Slides for Unit 5

An Online CNN Poll
1
Probabilistic Sampling
Methods
• Simple Random Sampling
• Each elementary unit in the population has an equal
chance of being selected for the survey
• Random Digit Dialing
• Pick telephone numbers at random
• Stratified Random Sampling
• Take a random sample from each strata
• Cluster Sampling
• Take a random sample of clusters and survey
everyone in the cluster
2
Non-Probabilistic
Sampling Methods
• Systematic Sampling
• Every nth person (whatever) is chosen
• Convenience Sampling
• Respondents who are willing and available are
selected
• Snowball Sampling
• Previously-identified respondents identify others
(“ask a friend”)
• Focus Groups and Expert Panels
3
Two Variables, x & y
Random
Experiment
x
y
Pick one person and
record their age
Pick 40 people and
record the average age
One Observation
Population
Population Mean
Pop. Variance
Shape of
Distribution
4
Sampling Distribution
_
of x
1. Mean (Expected Value)
2. Variance
3. Shape
_
• x has a t distribution if the sample size is large
5
Central Limit Theorem
Distribution
of x
Distribution
_
of x with
n=30
WHEN n  30,
_
x HAS A
t
DISTRIBUTION
6
Exercise #1
• The sign on the elevator says “maximum
capacity 2500 pounds or 16 persons.” Weights
of people who use the elevator is normally
distributed with mean 150 pounds and
standard deviation of 20 pounds. What is the
probability that 16 people weigh more than
2500 pounds?
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Sampling Distribution
_
of p
1. Mean (Expected Value)
2. Variance
3. Shape
_
• p is normally distributed if the sample size is
large (np5 and n(1-p) 5)
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Exercise #2
• In the population of all statistics students, the
fraction of students that fall asleep is 0.20. In a
class of 25, what’s the probability that more
than four fall asleep?
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Sampling Distribution
of b (regression coeff.)
1. Mean (Expected Value)
2. Variance
Requires homoskedasticity
and independent errors
3. Shape
• b has a t distribution if the sample size is large
(CLT for errors)
10
Use the t distribution!
• Always need to estimate
and
_
• So distribution of x and b have a t distribution
• Degrees of freedom
• Sample mean case: n-1 d.f.
• Note: just estimating one parameter (variance)
• Regression case: n-k-1 d.f.
• k=number of coefficients excluding the
intercept
• the “-1” captures the intercept
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t Critical Values
Degrees of
Freedom
Area in Upper Tail
1
0.10
3.078
0.05
6.314
0.025
12.706
0.01
31.821
0.005
63.656
2
1.886
2.920
4.303
6.965
9.925
3
1.638
2.353
3.182
4.451
5.841
1.310
1.697
2.042
2.457
2.750
1.282
1.645
1.960
2.326
2.576
…
30
…

12