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Sampling distribution of a sample mean

Sampling distribution of a sample mean. Shape of sampling distribution of depends on the population distribution. If population distribution is normal, then so is the distribution of sample mean.

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Sampling distribution of a sample mean

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  1. Sampling distribution of a sample mean • Shape of sampling distribution of depends on the population distribution. • If population distribution is normal, then so is the distribution of sample mean. • If a population has the N(,) distribution, then the sample mean x of n independent observations has the N(, ) distribution.

  2. Central Limit Theorem • What happens when the population distribution is not normal? • As we increase the number of observations that we use to draw our sample, the sampling distribution of x changes its shape

  3. N = 1 N = 2 N = 25 N = 10

  4. Central Limit Theorem • Draw a simple random sample of size n from any population with mean  and standard deviation . • When n is large, the sampling distribution of the sample mean x is approximately normal N(, ) • Applies to sum or averages

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