ENVS278 Chapter Notes - Chapter 15: Central Limit Theorem, Sampling Distribution, Sampling Error
8 Oct 2016
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The histogram above is a simulation of what we would get if we could see all proportions from all possible samples. This distribution is called the sampling distribution of the proportions. The histogram is unimodal, symmetric and is centered at p. To use a normal model, we need to specify two parameters: its mean and standard deviation. The center of the histogram is naturally at p, so we"ll put , the mean of the normal, at p. To find the standard deviation of the proportion of successes sd(p ), take the square root of (pq n). Sampling error (sampling variability): not really an error but a variability you would expect to see from one sample to another. In short, provided that the sampled values are independent and the sample size is large enough, the sampling distribution of p is modeled by a normal model with mean (p ) and standard deviation sd(p ) = (pq n).
