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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**Sample Statistics and Sampling Distributions**Sampling Distribution**Population Sample Parameters vs Statistics x ² s² s P p**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**Sample Statistics**Subject to sampling variation: sample statistics vary in value from one sample to another**Sampling Distribution**A listing of all possible values of the sample statistic, together with their associated probabilities.**Sampling Distribution**Of a sample mean Of a sample proportion**Sampling Distribution of a Sample Mean**The Central Limit Theorem**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**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**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]**Large Enough?**Rule of Thumb: np 5 and n(1-p) 5

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