RANDOM SAMPLING

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. SampleGallup 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 SRSCreate 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 selectionGive each student a numberSince 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 Calculator7 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 SampleDivide 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 kth element in the population to be part of your sample

List the students in AP Statistics alphabeticallyNumber the students

Randomly select a student

Choose every kth 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 SampleB) Stratified SamplingC)Cluster SamplingD)Systematic Random Sampling

To obtain a sample of those attending a basketball game, a researchers selects the 24th person through the door. Then, every 50th person after that is also included in the sample.

A)Simple Random SampleB)Stratified SamplingC)Cluster SamplingD)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.