lecture_5_1

# lecture_5_1 - Sampling distributions - for counts and...

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Sampling distributions for counts and proportions IPS chapter 5.1 © 2006 W. H. Freeman and Company

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Objectives (IPS chapter 5.1) Sampling distributions for counts and proportions Binomial distributions Sampling distribution of a count Sampling distribution of a proportion Normal approximation
Counts and Proportions Example 1 : A sample survey picks 2500 adults randomly. Asks if agree or disagree with “I like shopping”. The number of people who say ‘agree’ is a random variable X. Example 2 : A coin is tossed 10 times. See whether head or tail shows up. The number of heads is a random variable X.

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In both of these cases, X is a count of the occurrences of some outcome in a fixed number of observations. If the number of observations is n , then the sample proportion is which is also a random variable. Both counts and sample proportion are common statistics. In this section, we will look at their distribution. n X p / ˆ =
Binomial distributions Binomial distributions represent the distribution of number of successes in a series of n trials. The observations must meet these requirements: The total number of observations n is fixed in advance. Each observation falls into just 1 of 2 categories: success and failure. The outcomes of all n observations are independent. All n observations have the same probability of “success,” p . We record the next 50 births at a local hospital. Each newborn is either a boy or a girl; each baby is either born on a Sunday or not.

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We express a binomial distribution for the count X of successes among n observations as a function of the parameters n and p: B ( n,p ). The parameter n is the total number of observations. The parameter p is the probability of success on each observation. The count of successes X can be any whole number between 0 and n . A coin is flipped 10 times. Each outcome is either a head or a tail.
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## This note was uploaded on 05/09/2009 for the course PAM 2100 taught by Professor Abdus,s. during the Spring '08 term at Cornell.

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lecture_5_1 - Sampling distributions - for counts and...

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