1. An Online CNN Poll

2. 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

3. 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

4. Two Variables, x & y x y Random Experiment
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

5. Sampling Distribution of x_
1. Mean (Expected Value)
2. Variance
3. Shape
x has a t distribution if the sample size is large _

6. Distribution of x with n=30
Central Limit Theorem
Distribution of x with n=30 _
Distribution of x
WHEN n  30,
x HAS A
t DISTRIBUTION _

7. 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?

8. 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) _

9. Exercise #2
In the population of all statistics students, the fraction of students that fall asleep is In a class of 25, what’s the probability that more than four fall asleep?

10. 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)

11. 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 _

12. t Critical Values Degrees of Freedom Area in Upper Tail 0.10 0.05
0.025
0.01
0.005 1
3.078
6.314
12.706
31.821
63.656 2
1.886
2.920
4.303
6.965
9.925 3
1.638
2.353
3.182
4.451
5.841 … 30
1.310
1.697
2.042
2.457
2.750 
1.282
1.645
1.960
2.326
2.576