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Lecture_5

# Lecture_5 - Sampling Distributions How Likely Are the...

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Sampling Distributions How Likely Are the Possible Values of a Statistic? The Sampling Distribution

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Learning Objectives 1. Statistic vs. Parameter 2. Sampling Distributions 3. Mean and Standard Deviation of the Sampling Distribution of a Proportion 4. Standard Error 5. Sampling Distribution Example 6. Population, Data, and Sampling Distributions
Learning Objective 1: Statistic and Parameter A statistic is a numerical summary of sample data such as a sample proportion or sample mean A parameter is a numerical summary of a population such as a population proportion or population mean. In practice, we seldom know the values of parameters. Parameters are estimated using sample data. We use statistics to estimate parameters.

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Learning Objective 2: Sampling Distributions Example: Prior to counting the votes, the proportion in favor of recalling Governor Gray Davis was an unknown parameter . An exit poll of 3160 voters reported that the sample proportion in favor of a recall was 0.54. If a different random sample of about 3000 voters were selected, a different sample proportion would occur. The sampling distribution of the sample proportion shows all possible values and the probabilities for those values.
Learning Objective 2: Sampling Distributions The sampling distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take. Sampling distributions describe the variability that occurs from study to study using statistics to estimate population parameters Sampling distributions help to predict how close a statistic falls to the parameter it estimates

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Learning Objective 4: The Standard Error To distinguish the standard deviation of a sampling distribution from the standard deviation of an ordinary probability distribution, we refer to it as a standard error.
Learning Objective 6: Population Distribution Population distribution: This is the probability distribution from which we take the sample. Values of its parameters are usually unknown. They’re what we’d like to learn about.

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Learning Objective 6: Data distribution This is the distribution of the sample data. It’s the distribution we actually see in practice. It’s described by statistics With random sampling, the larger the sample size n , the more closely the data distribution resembles the population distribution
Learning Objective 6: Sampling Distribution This is the probability distribution of a sample statistic.

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Lecture_5 - Sampling Distributions How Likely Are the...

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