+ Homework READ p COMPLETE (p.227)  19, 21, 23, 25, 27-29, 31, 33, 35 CHECK your answers in the back of the book Please Complete the Following 2 nd Chance MC Chapter 3 – this Fri 10/26 & next Mon 10/29 during lunch Bonus Test Chapter 3 – this Fri 10/26 after school Chapter 4 Test Tues 11/6 Upcoming

+ Last Night’s Homework - Evens 4.12(a) Number the 33 complexes from 01 to 33 alphabetically. Go to the random number table and pick a starting point. Record two-digit numbers, skipping any that aren’t between 01 and 33 or are repeats, until you have 3 unique numbers between 01 and 33. (b) Starting at line 117 we read off the following numbers: 38 (ignore) (ignore) 85 (ignore) (ignore) 18. So we have picked: Fairington (16), Waterford Court (32) and Fowler (18). 4.14(a) Number the gravestones from to Go to the random number table and pick a starting point. Record 5-digit numbers, skipping any that aren’t between and or are repeats, until you have 395 unique numbers between and (b) Starting at line 127 we read off the following numbers: (ignore all numbers not in bold). So the first three gravestones picked are those numbered 43909, and (a) False—if it were true, then after looking at 39 digits, we would know whether or not the 40th digit was a 0. (b) True—there are 100 pairs of digits 00 through 99, and all are equally likely. (c) False— 0000 is just as likely as any other string of four digits. 4.18(a) To obtain an SRS, every tree would need to have an equal chance of being included in the sample. It is not practical to even identify every tree in the park. (b) This sampling method is biased because these trees are unlikely to be representative of the population. Trees along the main road are more likely to be damaged by cars and people and may be more susceptible to infestation. (c) The scientists can be confident that the actual percentage of pine trees in the area that are infected by the pine beetle is near 35% although there is always some error associated with using sampling to estimate population parameters. Check your Answers

+ Day 3 / 11 Chapter 4: Designing Studies Section 4.1Sampling and Surveys

+ Learning Objectives After this section, you should be able to… DESTINGUISH between simple random samples, stratified random samples, and cluster samples IDENTIFY advantages and disadvantages of each random sampling method EXPLAIN how undercoverage, nonresponse and question wording can lead to bias in sample surveys Section 4.1 Designing Samples

+ Paired Activity: Rolling Down the River When is a stratified random sample useful? 1. Complete the packet. Be deliberately random - clearly identify all 4 steps. 2. Plot your mean yield data on the board 3. Answer the questions on p.3 4. Repeat the process with the addition of a new irrigation system 5. When is it more useful to use stratified sampling? 6. When is it more useful to use a SRS?

+ Sampling and Surveys Stratified Random Sample SRS refers only to a simple random sample. The basic idea of sampling is straightforward: take a SRS fromthe population and use your sample results to gain information about the population. Sometimes there are statistical advantages to using more complex sampling methods. One common alternative to a SRS involves sampling importantgroups (called strata) within the population separately. These“sub-samples” are combined to form one stratified randomsample. Definition: To select a stratified random sample, first classify the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample.

+ Sampling and Surveys Stratified Random Sample When is a stratified random sample more usefulthan a SRS? when the individuals in each stratum are less variedthan the population as a whole iow, when you have identifiable groups of similarindividuals name three examples of when a stratified randomsample would be useful Student opinion at a high school – strata would be gradelevel

+ Sampling and Surveys Other Sampling Methods Although a stratified random sample can sometimesgive more precise information about a populationthan a SRS, both sampling methods are hard to use when populations are large and spread out over awide area. In that situation, we’d prefer a method that selects groups of individuals that are “near” one another. Definition: To take a cluster sample, first divide the population into smaller groups. Ideally, these clusters should mirror the characteristics of the population. Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample.

+ Sampling and Surveys Example: Sampling at a School Assembly Describe how you would use the following sampling methodsto select 80 students to complete a survey. (a) Simple Random Sample (b) Stratified Random Sample (c) Cluster Sample

+ Sampling and Surveys Check Your Understanding The manager of a sports arena wants to learn more about thefinancial status of the people who are attending an NBA basketballgame. He would like to give a survey to a representative sample ofthe more than 20,000 fans in attendance. Ticket prices for the gamevary a great deal: seats near the court cost over $100 each, whileseats in the top rows of the arena cost $25 each. The arena isdivided into 30 numbered sections, from 101 to 130. each sectionhas rows of seats labeled with letters from A (nearest to the court) toZZ (top row of the arena). Why might it be difficult to give the survey to an SRS of 200 fans? Which would be a better way to take a stratified random sample offans: using the lettered rows or numbered sections as strata? Why? Which would be a better way to take a cluster sample of fans: usingthe lettered rows or numbered sections as clusters? Why?

+ Bias ERROR favors certain outcomes Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent, or to the sampling method! There are many sources of bias

+ Voluntary response People choose to respond Usually only people with very strong opinions respond An example would be the surveys in magazines that ask readers to mail in responses. Other examples are call-in shows, American Idol, etc. Remember – the way to determine voluntary response is: Self-selection!!

+ Convenience sampling Ask people who are easy to ask Produces biased results An example would be stopping friendly-looking people in the mall to survey. Another example is the surveys left on tables at restaurants - a convenient method! The data obtained by a convenience sample will be biased – however this method is often used for surveys & results reported in newspapers and magazines.

+ Undercoverage some groups within the population are left out of the sampling process Suppose you take a sample by randomly selecting names from the phone book – some groups will not have the opportunity of being selected. People with unlisted phone numbers – usually high-income families People without phone numbers – usually low- income families People with ONLY cell phones – usually young adults

+ Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate telephone surveys 70% nonresponse People are chosen by the researchers, BUT refuse to participate. NOT NOT self-selected! This is often confused with voluntary response! Because of huge telemarketing efforts in the past few years, telephone surveys have a MAJOR problem with nonresponse! One way to help with the problem of nonresponse is to make follow contact with the people who are not home when you first contact them.

+ Response bias occurs when the behavior of respondent or interviewer causes bias in the sample wrong answers Suppose we wanted to survey high school students on drug abuse and we used a uniformed police officer to interview each student in our sample – would we get honest answers? Response bias occurs when for some reason (interviewer’s or respondent’s fault) you get incorrect answers.

+ Wording of the Questions wording can influence the answers that are given connotation of words use of “big” words or technical words Questions must be worded as neutral as possible to avoid influencing the response. The level of vocabulary should be appropriate for the population you are surveying

+ Source of Bias? 1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3-to-2 victory. A survey of 10 million people. George Gallup surveyed only 50,000 people and predicted that Roosevelt would win. The Digest’s survey came from magazine subscribers, car owners, telephone directories, etc. Undercoverage – since the Digest’s survey comes from car owners, etc., the people selected were mostly from high-income families and thus mostly Republican! (other answers are possible)

+ 2) Suppose that you want to estimate the total amount of money spent by students on textbooks each semester at FSU. You collect register receipts for students as they leave the bookstore during lunch one day. Convenience sampling – easy way to collect data or Undercoverage – students who buy books from on-line bookstores are included.

3) To find the average value of a home in Plano, one averages the price of homes that are listed for sale with a realtor. Undercoverage – leaves out homes that are not for sale or homes that are listed with different realtors. (other answers are possible)

+ Sampling and Surveys AP EXAM HINTS A student MUST 1) explain that the bias pushes the results one way or the other 2)Specify the direction!! It is NOT enough to say that bias exists…. However, unless you are explicitly ASKED TO IDENTIFY the type of bias present, DO NOT!!!! Just focus on the box above, state that the results are biased and state the direction.

+ Sampling and Surveys Inference for Sampling The purpose of a sample is to give us information about alarger population. The process of drawing conclusions about a population on thebasis of sample data is called inference. Why should we rely on random sampling? 1)To eliminate bias in selecting samples from the list of available individuals. 2)The laws of probability allow trustworthy inference about the population Results from random samples come with a margin of error that sets bounds on the size of the likely error. Larger random samples give better information about the population than smaller samples.

+ Sampling and Surveys Sample Surveys: What Can Go Wrong? Most sample surveys are affected by errors in addition tosampling variability. Good sampling technique includes the art of reducing allsources of error. Definition Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate. A systematic pattern of incorrect responses in a sample survey leads to response bias. The wording of questions is the most important influence on the answers given to a sample survey.

+ Homework READ p COMPLETE (p.227)  19, 21, 23, 25, 27-29, 31, 33, 35 CHECK your answers in the back of the book Please Complete the Following 2 nd Chance MC Chapter 3 – this Fri 10/26 & next Mon 10/29 during lunch Bonus Test Chapter 3 – this Fri 10/26 after school Chapter 4 Test Tues 11/6 Upcoming

+ Section 5.1 & 5.2 Designing Samples and Experiments 2005 AP Open Response Question 5 Read pp – quiz tomorrow on all of 5.2 through p. 364; may use notes p.364: p Homework

+ AP EXAM HISTORICAL PERSPECTIVE Open Response Questions - Chapter # # # # # # B # # B #3a 2003 B #4abd 2004 #2, 3d, 5b 2004 B #2, 6c 2005 #1bc, 5ac 2005 B # # B #5, 6f 2007 #2, 5a 2007 B # # B #4a 2009 # B #4, 6a 2010 B # B #2