Simple Random Samples Section 5.1.1

Starter What is the connection between the density curve of a standard normal distribution and a boxplot of the same distribution? –Specifically: What is the z-score of the median? –What are the z-scores of Q 1 and Q 3 ?

Objectives Describe the difference between a population and a sample Describe the difference between a census and a survey Describe what is meant by bias in a sample Describe what is meant by a –Voluntary Response Sample –Convenience Sample –Simple Random Sample Use a Table of Random Digits to construct a Simple Random Sample of specified size from a population

Population vs. Sample The entire group of individuals we want information about is called the population –Note that “individual” does not have to mean people The part of the population that we actually examine to gather information is called a sample.

Census vs. Survey A census is a study in which every member of a population provides information of interest. A survey is a study in which a sample of a population provides information of interest.

Commonly Used Sampling Methods Voluntary Response Sample –Commonly used in radio, tv, internet surveys –Respondents choose themselves to participate –People who feel negatively about the question are more likely to respond than those who do not Convenience Samples –Commonly used at places where people congregate Grocery stores, shopping malls, theaters, etc. –Questioners choose respondents by who happens to walk by

Bias in Sampling The design of a study is biased if it systematically favors certain outcomes. –A voluntary response sample is biased in that it favors negative outcomes regardless of the question. –A convenience sample is usually biased in that it favors the opinions of people in a certain location at a certain time. There is no guarantee that such opinion is representative of the population as a whole –In both cases a conscious choice is made to include/exclude a respondent We want a method in which the choice is random and does not depend on any individual

Simple Random Samples A Simple Random Sample (SRS) is a mechanical way of choosing a sample from a population so that all members have a chance of being chosen and no individual chooses to include/exclude a member of the population. Technically speaking: Choose a set of n individuals from a population in a manner such that all sets of size n had an equal chance of being chosen.

Mechanics of Creating an SRS Number all members of the population Use a table of random digits to select n members of the population –Enter the table on any line –Choose digits in groups sized according to the numbered population 10 or less individuals, use 1 digit: 0 – 9 11 – 100 individuals, use 2 digits: 00 – – 1000 individuals, use 3 digits: etc. –Ignore duplicate numbers or numbers beyond the population range

Example From a population of 25 individuals, choose an SRS of size 5 using this table: : choose 22: choose 39: ignore (there is not a person number 39) 50: ignore 34: ignore 05: choose 75: ignore 22: ignore (person number 22 is already in the SRS) 87: ignore 13: choose 06: choose

Class Example Choose an SRS of 6 members of this class using the numbered class roster and the table of random digits (Table B) in the back of the book. –Enter the table at line 116 –Write the numbers and names of the sample –There are 35 class members so choose two- digit groups from 01 – 35 –Choose:

Objectives Describe the difference between a population and a sample Describe the difference between a census and a survey Describe what is meant by bias in a sample Describe what is meant by a –Voluntary Response Sample –Convenience Sample –Simple Random Sample Use a Table of Random Digits to construct a Simple Random Sample of specified size from a population

Homework Read pages 245 – 253 Do problems 1 – 5