lecturenotesch7a

lecturenotesch7a - + + Chapter 7: Comparing Two Populations...

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+ + Chapter 7: Comparing Two Populations In Chapter 5, we learned that a population (fnite or BTs) can be represented as a box oF cards. We learned that the CM oF select- ing n cards at random w/replacement allows us to calculate probabilities. In Chapter 6, we learned how to inFer a Feature oF the box by using sample data. Also in Chapter 6 we learned how to predict Future draws From the box. In this Chapter, we extend some oF the ideas oF Chapter 6 to two boxes, representing two populations. Each box has its own p and q ; we distinguish these by adding subscripts. Thus, the frst box has p 1 and q 1 , while the second box has p 2 and q 2 . + 173
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+ + Before we turn to presenting formulas for es- timation, we will focus on some scientiFc is- sues. Namely, we will see that there are four distinct scientiFc situations that can lead to having two boxes, and we will learn the con- sequences of this. We get the four situations by combining two dichotomies: —The boxes can represent two Fnite popula- tions or two sequences of BTs; we never mix fnite with BTs . —The study can be controlled (the researcher employs randomization), or not, called obser- vational. I begin with an example of fnite populations and observational . This example appears on page 230 of the text. The Frst box is undergraduate men at the University of Wisconsin–Madison and the sec- University. (This study was published in 1988; I don’t recall when the data were collected.) + 174
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+ + Clearly these are both fnite populations. It is an observational study b/c the researcher did not assign men to university by randomiza- tion. (For example, i± Bubba and Bobby Lee are two men in the Texas box, they were not placed there by the researcher.) So, what is on each man’s card? The answer to the ±ollowing question: I± a woman is interested in dating you, do you generally pre±er ±or her: to ask you out; to hint that she wants to go out with you; or to wait ±or you to act. We see a di²culty: The response is a tri- chotomy. It turned out that o± the 207 men actually questioned, only a very small number (two, I recall) answered ‘wait.’ Thus, the researchers combined hint and wait to be an F, while ask was an S. + 175
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+ + Sampling? For mathematical reasons, we as- sume that cards are selected at random with replacement from each box and the selections in one box are independent of the selections in the other box. Discuss. Is this reasonable? Discuss. Well, even though we now doubt whether the assumption of random is reasonable, let us proceed as if it was. So, what happened in the study? Pop. Ask Other Total ˆ p Wis. 60 47 107 0.56 Tex. 31 69 100 0.31 Total 91 116 207 + 176
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+ + Now, p 1 is the proportion of all Wisconsin men who want to be asked. Following the ideas of Chapter 6, our point estimate of p 1 is ˆ p 1 = 0 . 56 and we could calculate a CI for p 1 . Similarly,
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This note was uploaded on 10/23/2009 for the course STAT STATS 301 taught by Professor Professorwardrop during the Fall '08 term at Wisconsin.

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lecturenotesch7a - + + Chapter 7: Comparing Two Populations...

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