# Copyright © 2010 Pearson Education, Inc. Slide 12 - 1.

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Copyright © 2010 Pearson Education, Inc. Slide 12 - 1

Copyright © 2010 Pearson Education, Inc. Slide 12 - 2 Solution: B

Copyright © 2010 Pearson Education, Inc. Chapter 12 Sample Surveys

Copyright © 2010 Pearson Education, Inc. Slide 12 - 4 Sample vs. Population The first idea is to draw a sample. We’d like to know about an entire population of individuals, but examining all of them is usually impractical, if not impossible. We settle for examining a smaller group of individuals—a sample—selected from the population. Sampling is a natural thing to do. Think about sampling something you are cooking—you taste (examine) a small part of what you’re cooking to get an idea about the dish as a whole.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 5 Sample vs. Population Example: Opinion polls are examples of sample surveys, designed to ask questions of a small group of people in the hope of learning something about the entire population. Professional pollsters work quite hard to ensure that the sample they take is representative of the population.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 6 Bias Sampling methods that, by their nature, tend to over- or under- emphasize some characteristics of the population are said to be biased. There is usually no way to fix a biased sample and no way to salvage useful information from it. The best way to avoid bias is to select individuals for the sample at random.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 7 Randomize Randomization can protect you against factors that you know are in the data. It can also help protect against factors you are not even aware of. Randomizing makes sure that on the average the sample looks like the rest of the population. Not only does randomizing protect us from bias, it actually makes it possible for us to draw inferences about the population when we see only a sample.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 8 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. Exception: If the population is small enough and the sample is more than 10% of the whole population, the population size can matter. The fraction of the population that you’ve sampled doesn’t matter. It’s the sample size itself that’s important.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 9 Census Sampling the entire population is a census. There are problems with taking a census: It can be difficult to complete a census—there always seem to be some individuals who are hard (or expensive) to locate or hard to measure; or it may be impractical - food. 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.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 10 Populations and Parameters Models use mathematics to represent reality. Parameters are the key numbers in those models. A parameter that is part of a model for a population is called a population parameter. Statistics are a summary found from the data.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 11 Notation We typically use Greek letters to denote parameters and Latin letters to denote statistics.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 12 Simple Random Samples We draw samples because we can’t work with the entire population. We need to be sure that the statistics we compute from the sample reflect the corresponding parameters accurately. A sample that does this is said to be representative.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 13 Simple Random Samples (cont.) Simple Random Sample (SRS) – Each person and combination of people have an equally likely chance of being selected. Example: There are 80 students enrolled in a class, you are to select a sample of 5. How can you select a SRS of 5 students using these random digits found on the internet: 05166 29305 77482?

Copyright © 2010 Pearson Education, Inc. Slide 12 - 14 Stratified Random Sampling SRS can take a lot of time, money and sometimes they are just impossible. There are others … Stratified Random Sampling – Populations are sliced into homogeneous groups (called strata) then a SRS is used in each strata. They are usually stratified by race, income, age, sex, etc. By stratifying sampling variability is reduced. Example: You are trying to find out what freshmen think of the food served on campus. You think men and women have a different opinion about the salad bar. Explain how a stratified random sample would be appropriate.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 15 Cluster Sampling Cluster Sampling is when the population is split into clusters and one or more clusters are randomly selected and a census is performed within each one. If the cluster represents the population fairly, the cluster sample will be unbiased. Example: You are still trying to find out what freshmen think about food services on campus. You were going to do a SRS and then a stratified sample, but you realized there are too many people on your list and it is too hard to find them. You realize the students that eat the food are all housed in 10 freshmen dorms. Explain how could you use a cluster sample.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 16 Multistage Samples Use two or more sampling techniques together. Example: I am trying to assess the reading level of our stats book. To assess the reading level I use sentences from in the book. I am worried that the later part of the book will have a higher reading level. I would strata by chapter and then randomly pick a page with in each chapter (cluster).

Copyright © 2010 Pearson Education, Inc. Slide 12 - 17 Systematic Sampling Systematic sampling is when I survey every 10 th person on a list. As long as the people on the list are random, I should have a good sample.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 18 Convenience Sample Convenience Sample – simply include individuals who are convenient. Example: Standing outside a mall and asking people to fill out a survey.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 19 Examples: We need to survey a random sample of the 300 passengers on a flight from San Fran to Tokyo. Name each sampling method described below: a. Pick every 10 th passenger as people board the plane. b. From the boarding list, randomly choose 5 people flying first class and 25 of the other passengers. c. Randomly generate 30 seat numbers and survey the passengers who sit there. d. Randomly select a seat position (right window, right center, right aisle, etc.) and survey all the passengers sitting in those seats.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 20 Who’s Sampling Frame - List of individuals from which the sample is drawn. Target Sample - These are the individuals for whom you intend to measure responses. You’re not likely to get responses from all of them. Nonresponse is a problem in many surveys. Your sample—the actual respondents. These are the individuals about whom you do get data and can draw conclusions. Unfortunately, they might not be representative of the sample, the sampling frame, or the population.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 21 Things to remember … Be careful in phrasing answers. It’s often a better idea to offer choices rather than inviting a free response. The best way to protect a survey from unanticipated measurement errors is to perform a pilot survey. A pilot is a trial run of a survey you eventually plan to give to a larger group. In a voluntary response sample, a large group of individuals is invited to respond, and all who do respond are counted. Voluntary response samples are almost always biased, and so conclusions drawn from them are almost always wrong. Voluntary response samples are often biased toward those with strong opinions or those who are strongly motivated. Since the sample is not representative, the resulting voluntary response bias invalidates the survey.

Copyright © 2010 Pearson Education, Inc. Slide 12 - 22 What Else Can Go Wrong? Work hard to avoid influencing responses. Response bias refers to anything in the survey design that influences the responses. For example, the wording of a question can influence the responses:

Copyright © 2010 Pearson Education, Inc. Slide 12 - 23 Homework: Pg. 288 1-27 odd, Very wordy. Be concerned with what type of survey, bias and how to write a good question.