Josie Burridge & Alyssa Pennacchi AP Statistics Chapter 12 Josie Burridge & Alyssa Pennacchi

Idea 1: Examine a Part of the Whole It is impractical to know about an entire population... We use smaller groups of individuals called Samples We use sample surveys that are designed to ask questions of a small group of people in the hope of learning something about the entire population

Idea 2: Randomize Biased sampling methods tend to over- or underemphasize some characters of the population. To prevent this we try to select people at random Randomizing is the best defense against bias because each individual is given a fair, random chance of selection

Bias Voluntary response bias: individuals choose on their own whether whether to participate in the sample Undercoverage: part of the population is given less representation than it has in the population Nonresponse: a large fraction of the sampled population fails to respond Response: anything in a survey designed to influence response

Idea 3: The Sample Size How large a random sample do we need for the sample to be reasonably representative of the population? It’s the size of the sample, not the size of the population, that makes the difference in sampling We could try to use a census-sampling an entire population-but problems can occur: It can be difficult to complete a census—there always seem to be some individuals who are hard to locate or hard to measure. Populations rarely stand still. Even if you could take a census, the population changes while you work, so it’s never possible to get a perfect measure.

Populations and Parameters A parameter that is part of a model for a population is called a population parameter. We use data to estimate population parameters. Any summary found from the data is a statistic. The statistics that estimate population parameters are called sample statistics.

Simple Random Sampling Because we cannot work with the entire population, we take samples If the statistics reflect the corresponding parameters accurately, the sample is said to be representative. We need to make sure every possible sample of the size we draw has an equal chance to be chosen A sample drawn this way is called a Simple Random Sampling

Types of Sampling Stratified Random Sample: the population is divided into several subpopulations, or strata, and random samples are then drawn from each stratum Cluster: entire homogenous groups, or clusters, are chosen at random Convenience: consists of individuals who are conveniently available Multistage: sampling schemes that combine several sampling methods Systematic: a sample drawn by selecting individuals systematically from a sampling frame

Exercise 15 An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to three hours for a 3-minute ride. Concerned about how patrons feel about this, they surveyed every 10th person in the line for the roller coaster, starting from a randomly selected individual. What kind of sample is this Systematic Is it likely to be representative? Yes, it is likely to be representative of those waiting for the roller coaster. What is the sampling frame? The sampling frame is the people waiting for the roller coaster on that day and that specific time.

Exercise 17 Two members of the PTA committee in Exercises 11 and 12 have proposed different questions to ask in seeking parents’ opinions. Question 1: Should elementary school-age children have to pass high stakes tests in order to remain with their classmates? Question 2: Should schools and students be held accountable for meeting yearly learning goals by testing students before they advance to the next grade?

Exercise 17 Answers Do you think the responses to these two questions might differ? How? What kind of bias is this? Yes, the first question is likely to be answered with a negative response while the second question will likely be answered with a positive response. It is a response bias--the questions are tailored to push responders to answer a specific way. Propose a question with more neutral wording that might better assess parental opinion. Should students be required to test at the end of each year over the knowledge they were taught in order to move to the next grade?