1. Unit 4 Gathering Data LESSON 4-2 - SAMPLING WHAT ARE GOOD WAYS AND POOR WAYS TO SAMPLE?

2. Learning Objectives: 1. Sampling Frame & Sampling Design 2. Simple Random Sample (SRS) 3. Choosing a Simple Random Sample 4. Margin of Error 5. Convenience Samples 6. Types of Bias in Sample Surveys

3. Learning Objective 1: Sampling Frame & Sample Design  The sampling frame is the list of subjects in the population from which the sample is taken, ideally it lists the entire population of interest  The sampling design determines how the sample is selected. Ideally, it should give each subject an equal chance of being selected to be in the sample.

5. Learning Objective 2: Simple Random Sampling (SRS)  Random Sampling is the best way of obtaining a sample that is representative of the population. (that’s what we ultimately want)  A simple random sample of ‘n’ subjects from a population is one in which each possible sample of that size has the same chance of being selected. (an equal opportunity employer survey)

7. Learning Objective 2: Simple Random Sampling (SRS) EXAMPLE: Your class has 36 students. Your teacher has 9 surveys that need to be completed by students in your class. Which of the following examples are a simple random sample? A) He rolls a die to tell him the row 1 to 6 and another die to tell him the seat 1 to 6 and does this 9 times. B) The 9 students sitting closest to the teacher’s desk are given a survey. C) The teacher has students put their names on torn pieces of paper (different sizes) and draws 9. D) The teacher numbers students 01 to 36 in the gradebook & uses a random number generator to pick 9. E) The teacher hands 9 surveys to the first 9 students through the door. SRS SRS

8. Learning Objective 3: Choosing a Simple Random Sample 78878 37220 62192 60719 91695 98768 04108 88086 36152 65396 51106 20535 85691 90223 29743 84623 93427 20130 40020 80350 06245 81677 55379 07717 50702 48306 02377 66724 00240 73132 81014 30812 81418 03040 91291 26539 20794 64587 06649 53906 This is a random number table. Notice numbers are chunked in sets of 5 to easily regroups EXAMPLE: Number off from 01 to ­36. And select a simple random sample of 6 students in your class. EXAMPLE: If sampling frame is 001 to 500, what would your first 5 samples be? (start in row 4)

10. Learning Objective 4: Margin of Error  Sample surveys are commonly used to estimate population percentages.  These estimates include a margin of error which tells us how well the sample estimate predicts the population percentage.  When a SRS of n subjects is used, the margin of error is approximately:

11. Learning Objective 4: Margin of Error A survey result states: “The margin of error is plus or minus 3 percentage points” or “+/- 3%” This means it is very likely (with 95% confidence) that the reported sample percentage is no more than 3% lower or 3% higher than the population percentage. EXAMPLE: President Obama’s current approval rating (as of 5-17-15) was 48% with a 3% margin of error. This means the actual approval rating for the entire country ranges anywhere from… 45% to 51%

12. EXAMPLE: The Gallup poll reported that 56% of Americans believed New Orleans will never completely recover from Hurricane Katrina. Find the approximate margin of error if:  A) n=200  B) n=800  C) n=3200 As sample size __________, the margin of error ________. increases Learning Objective 4: Margin of Error decreases

14. Convenience Sample: a type of survey sample that is easy to obtain  Unlikely to be representative of the population (results apply ONLY to the observed subjects)  Often severe biases result from such a sample Learning Objective 5: Poor Ways to Sample Example: Stand outside the __________ and survey the first ____ people who come by. library 15

16. Volunteer Sample: Most common form of convenience sampling  Subjects volunteer for the sample  Volunteers do not tend to be representative of the entire population Learning Objective 5: Poor Ways to Sample Example: Every receipt at a ____________ has a survey form that can be filled out for a ___% off coupon. restaurant 5

17. Learning Objective 6: Types of Bias in Sample Surveys A large sample does not guarantee an unbiased sample! Bias is the tendency to systematically favor certain parts of the population over others (might be purposeful or accidental)  Sampling Bias : bias resulting from sampling design, such as using nonrandom samples or having undercoverage (not enough of the right people) Example: A survey is done about parking at BCHS with ____ students. They are all __________. 10 sophomores

18. Learning Objective 6: Types of Bias in Sample Surveys  Nonresponse bias : occurs when some sampled subjects cannot be reached or refuse to participate or fail to answer some questions (too sensitive or just inattentive)  Response bias : occurs when the subject gives an incorrect response or the question is misleading or leading Example: A survey asks about ________________. 90% of the ____ students who responded, don’t do drugs. Example: A sample survey asks “You won’t vote for that unsupported bill SB-430, written by the bureaucrats will you?” student drug use15