STAT151 Lecture Notes - Lecture 12: Central Limit Theorem, Sampling Error, Sampling Distribution

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STAT151 Full Course Notes
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STAT151 Full Course Notes
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Sampling error - the error from using a sample to infer about a population, like mean or sd. Sample size and sample error: when n = n, y-(cid:271)a(cid:396) = . Mean and standard deviation of the sample mean: mean of sample mean, the mean of all possible sample means is the population mean, mean(y-bar(cid:524) = y-bar = . Sampling distribution of the sample mean for normally distributed variables. Involves 3 aspects: shape - the sampling distribution of all possible sample means are normally distributed, center - mean(y-(cid:271)a(cid:396)(cid:895) = , spread - sd(y-(cid:271)a(cid:396)(cid:895) = / (cid:374) Standardized version of y-bar (sample mean) z = (y-bar - (cid:524) / (cid:523) / n(cid:524) z-score = (sample mean - population mean) / (sample mean sd) Shape - normal: center - mean(y-bar) = . Assumptions and conditions of the sample mean distribution. Independence assumption - all samples must be independently drawn from the population: randomized condition - everything must be random.

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