Unit 4 Gathering Data LESSON SAMPLING WHAT ARE GOOD WAYS AND POOR WAYS TO SAMPLE?

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

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.

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)

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

Learning Objective 3: Choosing a Simple Random Sample 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)

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:

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 ) was 48% with a 3% margin of error. This means the actual approval rating for the entire country ranges anywhere from… 45% to 51%

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

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

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

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

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