STAT 200 Chapter 7 Inference for Distributions

Inferences based on the t-distribution (Section 7.1)

Let X be a random variable that follows a certain distribution with mean  and

 standard deviation . If we have a large enough sample size n, and other necessary

 conditions being satised, then the sampling distribution of the sample means X follows

 approximately N (, n ). If the underlying distribution of X is normal, the sampling

 distribution is normal regardless of the sample size.

In most situations, the value of the population standard deviation  is unknown. We

 will estimate  using the sample standard deviation s from a random sample, and

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