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Chapter9_STAT1100.ppt", filename="Chapter9_STAT1100.ppt", filename="Chapter9_STA

# Chapter9_STAT1100.ppt", filename="Chapter9_STAT1100.ppt", filename="Chapter9_STA

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Sampling Distributions Statistics for Management and Economics Chapter 9

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Objectives Sampling Distribution of the Mean Sampling Distribution of a Proportion Sampling Distribution of the Difference Between Two Means
Sampling Distributions… A sampling distribution is created by, as the name suggests, sampling . The sampling distribution of a statistic is the distribution of all possible values taken by the statistic when all possible samples of a fixed size n are taken from the population. It is a theoretical idea— we do not actually build it. The sampling distribution of a statistic is the probability distribution of that statistic. The method we will employ on the rules of probability and the laws of expected value and variance to derive the sampling distribution. Recall: statistic describes the sample, parameter describes the population!

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The law of large numbers Law of large numbers : As the number of randomly drawn observations ( n ) in a sample increases, the mean of the sample ( ) gets closer and closer to the population mean μ (quantitative variable). the sample proportion ( ) gets closer and closer to the population proportion ρ (categorical variable). x ˆ p
Sampling distribution When sampling randomly from a given population, the law of large numbers describes what happens when the sample size n is gradually increased. The sampling distribution describes what happens when we take all possible random samples of a fixed size n . Sampling distribution of [ insert statistic here ]

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Sampling distribution of x bar (the sample mean) We take many random samples of a given size n from a population with mean μ and standard deviation σ . Some sample means will be above the population mean μ and some will be below, making up the sampling distribution.
Sampling distribution of x bar Sampling distribution of x bar μ σ / n For any population with mean μ and standard deviation σ : The mean, or center of the sampling distribution of x bar, is equal to the population mean μ . The standard deviation of the sampling distribution is called the standard error , and defined as σ /√ n , where n is the sample size.

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Sampling distribution of x bar Mean of a sampling distribution of x bar: There is no tendency for a sample mean to fall systematically above or below μ, even if the distribution of the raw data is skewed. Thus, the mean of
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