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Probability

Probability. Sample Statistics and Sampling Distributions. Sampling Distribution. Population Sample Parameters vs Statistics  x  ²  s ² s P p. Proportions.

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Probability

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  1. Probability Sample Statistics and Sampling Distributions

  2. Sampling Distribution Population Sample Parameters vs Statistics  x ²  s² s P p

  3. Proportions Let P = population proportion of successes = x = # of successes in the population N population size Let p = sample proportion of successes = x = # of successes in the sample n sample size

  4. Sample Statistics Subject to sampling variation: sample statistics vary in value from one sample to another

  5. Sampling Distribution A listing of all possible values of the sample statistic, together with their associated probabilities.

  6. Sampling Distribution Of a sample mean Of a sample proportion

  7. Sampling Distribution of a Sample Mean The Central Limit Theorem

  8. The Central Limit Theorem No matter what the shape of the parent population, if a sample is randomly chosen with replacement from a population with mean, , and standard deviation, , then the sampling distribution of a sample mean, x, is approximately NORMAL, if the sample size is large enough; it will have numerical summary measures: x= and x = /n

  9. Large Enough? The Alternative Rule of Thumb: Suspected Pop’n ShapeRequired Sample Size Normal n  1 Symmetric n  15 Moderately skewed n  30 Severely skewed n  60

  10. Sampling Distribution of a Sample Proportion If a sample is chosen randomly with replacement from a population with a true proportion, P, then the sampling distribution of a sampling proportion, p, is approximately NORMAL, if the sample size is large enough; it will have numerical summary measures: p=P and p = sqrt[P(1-P)/n]

  11. Large Enough? Rule of Thumb: np  5 and n(1-p)  5

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