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Unformatted text preview: + + Chapter 15: Inference for One Numerical Population This chapter extends ideas from Chapter 6 for a dichotomous response to a numerical response. We will learn estimation and hy pothesis testing in Chapter 15, but not pre diction. (Prediction is discussed in the text, but we dont have enough time for it.) A key discovery in Chapters 5 and 6 is that a population might be determined by a number, p . (For a finite population, obviously, N and p determine the box and we found that often we can ignore N . For trials, if we have BTs then they are determined by p .) In Chapter 15, we will see that a population is given by a picture. If A picture is worth 1,000 words, you will be unsurprised to learn that inference in Chapter 15 has complica tions that did not arise in Chapter 6. + 241 + + There are actually two types of pictures for a population in Chapter 15, one for counting and one for measuring. We will begin with a phony example of a count population. (Dis cuss why phony examples are good.) In ad dition, we will pretend to be the all knowing Nature. A finite population consists of 100,000 house holds. For each household, the variable of in terest is The number of cats that live with the household. Once one settles on a defini tion of what it means for a cat to live with a household, one simply interviews a member of each household, who counts and reports its number of cats. To make the arithmetic easy, lets suppose that 10,000 households have 0 cats; 50,000 households have 1 cat; 30,000 households have 2 cats; and 10,000 households have 3 cats. + 242 + + We can represent this finite population as a box containing N =100,000 cards, one for each household. On a households card is its value of the response. We can summarize the contents of the box with the following table. Number of Number of Proportion of cats households households 10,000 0.10 1 50,000 0.50 2 30,000 0.30 3 10,000 0.10 Consider our usual CM: Select one card at random from the box. Let X denote the num ber on the selected card. The sampling dis tribution of X is given by the following table. x P ( X = x ) 0.10 1 0.50 2 0.30 3 0.10 Total 1.00 + 243 + + Next, we draw the probability histogram of the sampling distribution of X . Note that = 1; thus, the height of each rectangle equals the probability of the number at the center of the rectangle. Number of Cats 0.1 0.2 0.3 0.4 0.5 0 1 2 3 For future reference, for this population, = 1 . 40 and = 0 . 80. We have two equivalent ways to represent the population: the sampling distribution in the table above and the probability histogram. As we shall see, for a measurement response, our only choice is a picture. Thus, for simplicity, we choose to represent a count population by its probability histogram....
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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.
 Fall '08
 ProfessorWardrop
 Statistics

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