Section 5.1 Continued

 A simple random sample (SRS) of size n contains n individuals from the population chosen so that every set of n individuals has an equal chance of being selected.

 Example: SRS or not?  I want a sample of nine students from the class, so I put each of your names in a hat and draw out nine of them. ▪ Does each individual have an equal chance of being chosen? ▪ Does each group of nine people have an equal chance of being chosen?

 Example: SRS or not?  I want a sample of nine students from the class but I know that there are three juniors and 17 seniors in class, so I pick one junior at random and eight seniors. ▪ Does each individual have an equal chance of being chosen? ▪ Does each group of nine people have an equal chance of being chosen?

 Better than a hat: computers.  Software can choose an SRS from a list of the individuals in a list.  Not quite as easy as software, but still better than a hat: a table of random digits

 A table of random digits is a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with two properties:  Each entry in the table is equally likely to be any of the ten digits 0 through 9.  The entries are independent of each other. (Knowing one part of the table tells you nothing about the rest of the table.)  A table of random digits is a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with two properties:  Each entry in the table is equally likely to be any of the ten digits 0 through 9.  The entries are independent of each other. (Knowing one part of the table tells you nothing about the rest of the table.)

 Table B in the back of your book.

 Each entry is equally likely to be 0 – 9.  Each pair of entries is equally likely to be 00 – 99.  Each triple of entries is equally likely to be 000 – 999.  And so on…

 Example: Using a random digit table.  Read on page 276 the example 5.4

 A stratified random sample first divides a population into groups of similar individuals called strata. Then separate SRS’s are chosen from each group (stratum) and combined to make the full sample.

 Practice problems:  7-12 (p. 274 & 279)

 Choosing samples randomly eliminates human bias from the choice of sample, but…  What problems might remain? Brainstorm.

 Undercoverage  Having an inaccurate list of the population ▪ Ex: Who is excluded from a survey of “households”? ▪ Who is excluded from a telephone survey?

 Nonresponse  Occurs when selected individuals cannot be contacted or refuse to cooperate

 Which problem (undercoverage or nonresponse) is represented?  It is impossible to keep a perfectly complete list of addresses for the U.S. Census  Homeless people do not have addresses  In 1990, 35% of people who were mailed Census forms did not return them.

 Results may be influenced by behavior of either the interviewer or the respondent

 How might response bias show up in these situations?  A survey about drug use or other illegal behavior  Questions asking people to recall events, like: “Have you visited the dentist in the last six months?”

 The wording of questions can often lead to bias  “It is estimated that disposable diapers account for less than 2% of the trash in today’s landfills. In contrast, beverage containers, third-class mail, and yard wastes are estimated to account for 21% of the trash in landfills. Given this, in your opinion, would it be fair to ban disposable diapers?”

 “Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?”  “Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened?”

 “Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?” 22% said possible  “Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened?” 1% said possible

 Even if we can eliminate most of the bias in a sample, the results from the sample are rarely exactly the same as for the population  Each different sample pulls different individuals, so results will vary from sample to sample  Results are rarely correct for the population

 Since we use random sampling, we can use the laws of probability (later chapters!)  We’ll be able to figure out the margin of error (also in later chapters)

 Just know now: larger random samples give more accurate results than smaller samples.