David B. Howell
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A. Objectives—students will be able to
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1. define sample;
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2. describe and give examples of random sample;
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3. Iist factors compromising randomness;,
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4. describe variations among samples;,
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5. describe how changing sample size affects variation among several samples;
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6. select a sample size to estimate a population characteristic with confidence.
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B. The experimental questions—What percent of the population watches MTV? What percent of the population goes to bed before 10:30? (Or, perhaps, what percent of the students’ parents have visited the school?)
C. Issues, and some possible resolutions—
[It would be interesting and challenging to try to define the population as larger than the student body. (CAUTION: Hot everyone reacts positively or gracefully to being polled about almost anything! Before you prepare to have students poll outside the school population, by telephone or in any other way, get administrative approval.) If the class is up to that challenge, there will be substantial discussion about how to choose samples, how to deal with the random issue, what size sample to pick, how to poll the samples, etc. We want students to maximize the size and general nature of the population that they can reasonably sample. But predicting Connecticut’s MTV audience on the basis of a sample of a math class of 14-year-old urban students will hopefully strike the students as risky! And developing a reasonably accessible, even moderately random, sample of the American population should strike students as beyond their resources.]
D. Observations and discussion to Objectives—
On what basis did you choose the sample size? If we have enough different samples to “pool,” let’s do the same kind of analysis we did with Lesson 5. In any event, since we are dealing with a larger and more general population than our own school peers, is there any change in our feelings of confidence about predictions based on samples? Can we identify other factors that impact the change? [Difficulty with or uncertainty about randomness should be one—the larger the population and characteristics that might be studied, the more difficult it is to solve practical problems of random selection.]