Chapter 9: Means and Proportions as Random Variables

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Chapter 9 Means and Proportions as Random
Variables

• 9.1 Understanding dissimilarity among samples
• 9.2 Sampling distributions for sample
  proportions
• 9.3 What to expect of sample means
• 9.4 What to expect in other situations Central
  Limit Theorem
• Etc.

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Chapter 9 dependencies
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9.1 Understanding dissimilarity among samples
Suppose we have a population with known
characteristics (as in your lab). We propose to
pick a random sample from this population. The
science of probability can describe for us the
random behavior of this sample.
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9.1 contd Statistics is Probability in
reverse

On the other hand, if we have a population with
unknown properties, suppose we select a sample at
random. In Statistics, we use certain
characteristics (statistics) of the sample to
learn about the properties (parameters) of the
population. Probability Describe sample
behavior from population characteristics. Statisti
cs Infer population behavior from sample
characteristics by applying probability logic in
reverse.
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Probability Statement
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Statistics Statement
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9.2 An example involving proportions
Recent studies have shown that about 20 of
American adults fit the medical definition of
being obese. A large medical clinic would like
to estimate what percent of its patients is
obese, so it takes a random sample of 100
patients and finds that 18 are obese. Suppose
that in truth, the same percent holds for the
patients of the medical clinic as for the general
population, 20. (Problem 9.11, page 281)