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. It is a random variable. If the number of observations is n , then the sample proportion of this outcome 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 . Do the random variables in example 1 & 2 meet the requirements of binomial distributions?

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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 ).
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