Sampling Distribution Notation, A sample is large if the interval [p

Sampling Distribution Notation, A sample is large if the interval [p 3 σ p ^, p + 3 σ p ^] lies wholly within the interval [0, 1]. Consider the sampling distribution of the sample mean _ X when we take samples of size n from a population with mean μ and variance σ 2 . Moreover, the sampling distribution of the mean will tend towards normality as (a) the population tends toward normality, and/or (b) the sample size increases. If the population distribution is already approximately normal, a sample size of 30 will produce a sampling distribution that is approximately normal. Sampling distributions play a critical role in inferential statistics (e. Random sampling is assumed, but that is a completely separate assumption from normality. Hence, we need to distinguish between the analysis done the original data as opposed to analyzing its samples. Uh oh, it looks like we ran into an error. We refer to the above sampling method as simple random sampling. .

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