An Online CNN Poll

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

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

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

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

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 _

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?

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) _

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?

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)

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 _

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