Chapter 2 Lesson 2.2b Collecting Data Sensibly 2.2: Sampling

Methods of selecting random samples Simple Random Sample (SRS) A sample of size n is selected from the population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. every member of population has equal chance of being in sample (also, every sample is equally likely) A simple random sample does NOT guarentee that the sample is representative of the population. Suppose a local school has 2000 students. We want to survey 100 students about the current cell phone policy. A sample of students can be selected by putting each students ’ name on individual (but identical) slips of paper and placing them in a large container. After mixing well, randomly select 100 names from the container, one at a time. This is an example of a Simple Random Sample (SRS) It has to be possible for all 100 students in the sample to be seniors – or any other combination of students!

Simple Random Sample (SRS) continued A sample of size n is selected from the population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. Sampling frame – list of all the objects or individuals in the population. Methods of selecting random samples Another way to select a simple random sample is to create a list of all the students in the school (called a sampling frame). Number each student with a unique number from 1 to Use a random digit table or random number generator (a calculator or computer software) to select the 100 students for the sample.

Simple Random Sample (SRS ) continued A sample of size n is selected from the population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. Although sampling with and without replacement are different, they can be treated as the same when the sample size n is relatively small compared to the population size (no more than 10% of the population). Methods of selecting random samples Most often sampling is done without replacement. That is once an individual or object is selected, they are not replaced and cannot be selected again. Sampling with replacement allows an object or individual to be selected more than once for a sample.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Important Note: the Sample Size How large a random sample do we need for the sample to be reasonably representative of the population? It’s the size of the sample, not the size of the population, that makes the difference in sampling. Exception: If the population is small enough and the sample is more than 10% of the whole population, the population size can matter. The fraction of the population that you’ve sampled doesn’t matter. It’s the sample size itself that’s important.

Methods of selecting random samples Stratified Random Sample Population is divided into non-overlapping subgroups called strata Simple random samples are selected from each stratum Strata are groups that are similar (homogeneous) based upon some characteristic of the group members. Instead of a simple random sample to answer our survey about the cell phone policy at school, suppose we were take four simple random samples of size 25 from each grade level, freshman, sophomore, junior, and senior. This would be an example of a Stratified Random Sample

Methods of selecting random samples Cluster Sampling Population is divided into non-overlapping subgroups called clusters Randomly select clusters and then all the individuals in the clusters are included in the sample It is best if the clusters are heterogeneous subgroups from the population. Let ’ s look at another way to select a sample of students to answer our survey on the current cell phone policy at our school. One way to do this would be to randomly select 5 classrooms during 2 nd period. Survey all the students in those rooms! This is an example of a Cluster Sample

Methods of selecting random samples Systematic Sampling Sometimes we draw a sample by selecting individuals systematically. For example, you might survey every 10th person on an alphabetical list of students. To make it random, you must still start the systematic selection from a randomly selected individual. When there is no reason to believe that the order of the list could be associated in any way with the responses sought, systematic sampling can give a representative sample. Suppose we randomly select a number between 1 and 20. Using a alphabetical list of students at our school, select the student whose name is at that number in the list. Then choose every 20 th student from there. This is an example of a Systematic Random Sample

Identify the sampling design 1)The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, medium public, medium private, large public, and large private). Then they randomly selected 3 colleges from each group. Stratified random sample

Identify the sampling design 2) A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks. Cluster sampling

Identify the sampling design 3) A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10 th customer after them, to fill it out before they leave. Systematic sampling

Homework Reading Notes 2.3 Pg.46: #2.14, 2.16, 2.18, 2.19, 2.31 Practice Problems Handout