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# slide4 - Sampling distributions The probability...

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1 Sampling distributions The probability distribution of a statistic is called a sampling distribution. : the sampling distribution of the mean X n n ... n ... n X ... X X X 2 2 2 2 2 X X n 2 1 σ σ σ σ σ µ µ µ µ µ = + + + = = + + + = + + + = 2 The Central Limit Theorem When n is sufficiently large (i.e. greater than 15), the sample mean follows approximately a normal distribution: ~ , X N n σ µ

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3 Example 1 An electronics company manufactures resistors that have a mean resistance of 100 and a standard deviation of 10 . The distribution of resistance is normal. Find the probability that a random sample of n =25 resistors will have an average resistance less than 25 . 4 Example 2 Suppose that a random variable X has a continuous uniform distribution Find the distribution of the sample mean of a random sample of size n=40. = otherwise , 0 6 x 4 , 2 / 1 ) x ( f
5 Sampling distribution If we have two independent populations with means µ 1 and µ 2 and variance σ 1 2 and σ 2 2 , and if and are the sample means of two independent random samples of sized n 1
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