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5.1: Introduction to Sampling Distributions
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This chapter is devoted to studying sample statistics as random variables, paying close attention to probability distributions. Recall for each random variable, an underlying random experiment will be conducted and a value is assigned, measured, or computed for each possible outcome. These are the values the random variable is said to take on, and the probability of the values occurring is determined, forming a probability distribution.
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5.2: Sampling Distribution of Sample Means
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To construct a sampling distribution, we must consider all possible samples of a particular size,\(n,\) from a given population. This is more complicated than studying the entire population since considering every possible sample requires studying every member of the population. In practice, statisticians do not construct sampling distributions; instead, they use inferential statistics to learn about a population by studying a sample, a subset of the population, not the entire population itself.
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5.3: Sampling Distribution of Sample Proportions
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The sampling distribution of sample proportions is a particular case of the sampling distribution of the mean. We can be more specific by looking at the binomial distribution which is closely related to the sampling distribution of sample proportions.
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5.4: Sampling Distribution of Sample Variances - Optional Material
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For a particular population, the sampling distribution of sample variances for a given sample size n is constructed by considering all possible samples of size n and computing the sample variances for each one. The values of the sample variances are the values that our random variable takes on. We then build the probability distribution with the understanding that the sampling method is a simple random sampling. We understand the sample variances as a continuous random variable.