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# handout_5_1 - 5.1 Sampling Distributions for Counts and...

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5.1 Sampling Distributions for Counts and Proportions link between Chapter 4 (probability theory) and rest of book “Statistical inference draws conclusions about a population or process on the basis of data. The data are summarized by statistics such as means, proportions, and the slopes of least-squares regression lines. When the data are produced by random sampling or randomized experimentation, a statistic is a random variable that obeys the laws of probability theory. The link between probability and data is formed by the sampling distributions of statistics. A sampling distributions shows how a statistic would vary in repeated data production. That is, a sampling distribution is a probability distribution that answers the question ‘What would happen if we did this many times?’” (334) A statistic from a random sample or randomized experiment is a random variable. The probability distribution of the statistic is its sampling distribution . The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. The population distribution of a variable is the distribution of its values for all members of the population. The population distribution is also the probability distribution (sampling distribution ) of the variable when we choose one individual at random from the population. EX consider the heights of young women suppose the population = 1000/ then suppose take SRS of size n = 1 population distribution→ 1000 possible values sampling distribution→ 1000 possible samples of size 1 from population of 1000 sampling distribution→ 1000 possible values The distribution of heights of young women (18-24) is N(64.5, 2.5). Select a young woman at random and measure her height (random variable X). In repeated sampling X will have the same N(64.5, 2.5) distribution. population distribution= sampling distribution when we choose one individual at random from population

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5.1 nationwide random sample of 2500 adults ask if agree or disagree with: “I like shopping.” 1650 agreed random variable X is a count of the occurrences of some outcome in a fixed # of observations sample proportion : p ˆ = X/n p ˆ = (1650/2500) = 0.66 The binomial distributions for sample counts The binomial setting - four components
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## This note was uploaded on 02/01/2010 for the course PAM 2100 taught by Professor Abdus,s. during the Spring '08 term at Cornell.

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handout_5_1 - 5.1 Sampling Distributions for Counts and...

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