POPULATION- the entire group of individuals that we want information about SAMPLE- the part of the population that we actually examine in order to gather information about the population

Population vs. Sample Gallup finds unemployment at 10.1% in September The findings were based on more than 18,146 phone interviews (random digit dialing) with U.S. adults aged 18 and older POPULATION: all U.S. adults ages 18 and older who have telephones SAMPLE: 18,146 U.S. adults with telephones

SIMPLE RANDOM SAMPLE (SRS) A SRS (of size n) is selected from a population in a way that every different possible sample of size n has the same probability of being selected

Constructing an SRS Create a list of the sampling frame Give each object a number Use a random number table to select sample An Example: Randomly select 4 students from our AP Stat class List all students available for selection Give each student a number Since the largest number of students that we can select only has two digits, we will take numbers in groups of 2 (start on line 130 of Table B)

Line 130 of the Random Number Table

Generating Random Numbers on the TI Graphing Calculator 7  Math, rand, enter (change random seed #) Math >>> 5 (PRB) randInt (min,max) Note: If a number is selected more than once, ignore it

Stratified Random Sample The population is divided into at least two distinct groups (strata). A simple random sample of a certain size is drawn from each strata. Often, the size is chosen by using the actual percentage of occurrence in the overall population Example: Divide class into males and females and randomly select from each gender in the proportion that they occur in the population (class). Think of some other variables that we could stratify our class by

Cluster Sample Divide the population into subgroups (clusters) Select clusters at random Include all individuals in the selected clusters in your study Example: Randomly select homerooms and then include all students in the homerooms in the sample In class, randomly select a row, include all students in the row to be in the sample Multi-Stage Cluster Sample

Systematic Sampling The elements in the population should already be arranged in some natural sequential order Choose every k th element in the population to be part of your sample List the students in AP Statistics alphabetically Number the students Randomly select a student Choose every k th student depending on the size of your sample K = N/n = ________ Round down. Choose every _______ student

All freshman at a university are enrolled in 1 of 30 sections of a freshman seminar course. To select a sample of freshman at this university, a researcher selects 4 sections of the freshman seminar course at random and all students in the 4 selected sections are included in the sample. A) Simple Random Sample B) Stratified Sampling C) Cluster Sampling D) Systematic Random Sampling

To obtain a sample of those attending a basketball game, a researchers selects the 24 th person through the door. Then, every 50 th person after that is also included in the sample. A) Simple Random Sample B) Stratified Sampling C) Cluster Sampling D) Systematic Random Sampling

How can we select a simple random sample from the previous example?

The NBA could number an alphabetical list of players from 1 to 348. They could use a random number generator on a calculator to generate 58 UNIQUE random numbers from 1 to 348. The players corresponding to those 58 numbers would be asked to participate.