Chapter 4: Designing Studies

1. Chapter 4:Designing Studies 4.1: Sampling and Surveys

2. Population and Sample: The entire group of individuals that we want information about is called the population.A sample is a part of the population that we actually examine in order to gather information. Be specific! EX: High school seniors vs Perry high school seniors Sampling versus a Census: Sampling involves studying a part in order to gain information about the whole.A census attempts to contact every individual in the entire population. Larger the sample, the better the results. EX 1: Identify the population and sample in each of the following settings. a) The student government at a high school surveys 100 students at the high school to get their opinions about a change to the bell schedule. b) The quality control manager at a bottling company selects a sample of 10 cans from the production line every hour to see whether the volume of the soda is within acceptable limits. Pop: Students at a high school Sample: 100 students surveyed Sample: 10 cans inspected Pop: all cans in the bottling company

3. Convenience Sampling: A convenience sample chooses the individuals easiest to reach.This will typically result in a biased sample of like-minded individuals. • Bias: The design of a study is biased if it would consistently underestimate or consistently overestimate the value you want to know. • When asked to describe how the design of a study leads to bias: • 1. identify the problem with the design • 2. explain how the problem would lead to an under or overestimate • Voluntary Response Sample: A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples are biased because they attract people who feel strongly about an issue, and who often share the same opinion. Some surveys allow people to respond more than once. EX: American Idol or Dancing with the stars.

4. EX 2: In May 2010 the L.A. City Council voted to ban most travel and contracts with state of Arizona to protest Arizona’s new immigration law. The Los Angeles Times conducted an online poll that asked whether the City Council was right to pass a boycott of Arizona. The results showed that 96% of the 41,068 people in the sample said, “No”. What type of sample did he Times use in this poll? Explain how this sampling method could lead to bias in the poll results. They used a voluntary response sample. The people who participated in the poll probably feel much more strongly about the issue than those who chose not to participate. The value of 96% is likely to be an overestimate.

5. Simple random sample (srs) Simple Random Sample: A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. Most common sampling method When describing how you would set up your SRS, be as clear as possible! Give specific details.Nothing is implied. If repeats are not allowed, it needs to be mentioned. *The easiest way to choose an SRS is to write names on identical slips of paper, put the slips in a hat, mix them well, and pull out slips one at a time until you have n of them.

6. Choosing an SRS-Random digits table 01 12 07 17 02 08 13 18 03 09 19 14 04 10 15 20 05 11 21 16 06 a) Use Table D at line 101 to select an SRS of 3 stores. Choosing an SRS: Step 1: Label. Assign a numerical label to every individual in the population. You need each term to have the same number of digits Step 2: Table or Calculator. Use Table D to select labels at random or use the random number generator on your calculator. 1 9 2 2 3 9 5 0 3 4 0 5 7 5 6 2 8 7 1 3 Star Jewelers, Carter’s, Mrs. Fields

7. Choosing an srs - technology b) Use technology to select an SRS of 3 stores. Click “math” then go over to “PROB” and select option #5 “randInt(“ This is really helpful when you want to select multiple # and don’t want repeats OLD Calc: NEW Calc: Low # high # #20: Vitamin World #4: Barnes and Noble #11: Hagger Hit “enter” over and over again until you have 3 unique numbers

8. Other types of Samples Stratified Random Sample: To select a stratified random sample, first divide the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRS's to form the full sample. We take “some from all.” Cluster Sample: Classify the population into groups of individuals that are located near each other, called clusters. Then choose a SRS of the clusters. All individuals in the chosen clusters are included in the sample. We take “all from some.” Systematic Random Sample: To get a systematic random sample of students as they enter the auditorium at an all-school assembly, randomly choose a number from 1 to 10 to be the first member of the sample and then survey every 10th student after that. For example, if Student 9 was selected, then survey student number 9, 19, 29, and so on.

9. EX4: A farmer has just cleared a new field for corn. It is a unique plot of land in that a river runs along one side. The corn looks good in some areas of the field but not others. The farmer is not sure that harvesting the field is worth the expense. He has decided to harvest 10 plots and use this information to estimate the total yield. Based on this estimate, he will decide whether to harvest the remaining plots. A. Method Number One: Convenience Sample The farmer began by choosing 10 plots that would be easy to harvest. They are marked on the grid below: Since then, the farmer has had second thoughts about this selection and has decided to come to you (knowing that you are an AP statistics student, somewhat knowledgeable, but far cheaper than a professional statistician) to determine the approximate yield of the field. You will still be allowed to pick 10 plots to harvest early. Your job is to determine which of the following methods is the best one to use – and to decide if this is an improvement over the farmer’s original plan.

10. B. Method Number Two: Simple Random Sample Use your calculator or a random number table to choose 10 plots to harvest. Mark them on the grid below, and describe your method of selection Randomize the calc: Fill in the 10 squares you randomly selected 1 11 21 31 41 51 61 71 81 91 10 20 30 40 50 60 70 80 90 100 X X X

11. C. Method Number Three: Stratified Sample Consider the field as grouped in vertical columns (called strata). Using your calculator or a random number table, randomly choose one plot from each vertical column and mark these plots on the grid. Fill in the square you randomly selected in each column 1 2 3 4 5 6 7 8 9 10 X X X X

12. D. Method Number Four: Stratified Sample Consider the field as grouped in horizontal rows (also called strata). Using your calculator or a random number table, randomly choose one plot from each horizontal row and mark these plots on the grid. Fill in the square you randomly selected in each row 1 2 3 4 5 6 7 8 9 10 X X X X

13. OK, the crop is ready. Below is a grid with the yield per plot. Estimate the average yield per plot based on each of the four sampling techniques. Mean: Find the sum of your 10 squares and then divide by 10 Estimate: multiply your mean by 100

14. Method C (A stratified random sample with the strata being vertical columns) was the best method. • The purpose of a sample is to give us info about the population. Even if it is a truly random sample, the results could be different from the population. I could even take several different samples and get different results each time. This is accounted for by the margin of error.

15. Part II: The farmer was very impressed with the results of your study and seeks to improve the yield of that part of the field the following year. Believing that irrigation is the answer, a new system was installed. The following year’s yield was: BEFORE AFTER How would that change what sampling method you would use? A SRS would be better since all of the plots are similar

16. Undercoverage and Nonresponse • 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. • Other Forms of Bias • The behavior of the respondent or of the interviewer can cause response bias in sample results. For example, people may respond differently in person than they would on the phone or if the survey was given anonymously. • The wording of questions is the • most important influence on the • answers given to a sample survey. • Confusing or leading questions can • introduce strong bias, and even minor • changes in wording can change a • survey’s outcome.

17. EX 5: In 1988 Shere Hite published a survey result, in which she claimed that 70% of women who had been married 5 years or more were having extramarital affairs. Hite’s Survey was sent to 100,000 women, and her conclusions were based on the 4500 women who responded. What was the nonresponse rate for this study? How might this nonresponse have affected the results of the survey? Nonresponse rate: The nonresponse rate is 95.5%. If the women who responded to the survey differ from those who did not respond, the proportion of .7 will not be accurate.

18. Just a heads up, the multiple choice for the chapter 4 test are tricky. If you are looking for extra practice problems, there are 2 two multiple choice progress checks open under “My AP Classroom” Unit 3 Progress A check covers 4.1 Unit 3 Progress B check covers 4.2 This is optional, but HIGHLY encouraged.