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Section5.4-students_SP11

# Section5.4-students_SP11 - Section 5.4 Distribution of the...

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5/25/2011 1 Distribution of the Sample Mean General Result: Let X 1 , X 2 , ... , X n denote a Random Sample from a Large Population with E[ X i ] = and V[ X i ] = 2 (Called n independent and identically distributed RV’s ). Then, 1. 2. Section 5.4 1 Issue: Variability in the Sample Means over repeated sampling NOTE: The effect of increasing sample size on the Sampling Variance of the Sample Mean. Probability Distribution of the Sample Mean We will focus on the probability distribution of in two situations: 1. X i N( , 2 ) “No approximation needed.” 2. Large sample size n, “Limiting Case”: n when X i ’s have an arbitrary (but same) underlying probability distribution First Case : Sample from a Normal population In this case: 2

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5/25/2011 2 3 Central Limit Theorem (CLT) Second Case : In this case, when n is sufficiently large, 4
5/25/2011 3 5 Summary Statistics for 500 Repeated Samples of Averages of Various Sample Sizes Underlying Population: Bernoulli (p=.75) 6 1 0 500 400 300 200 100 0 C15 Frequency Mean 0.736 StDev 0.4412 N 500

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Section5.4-students_SP11 - Section 5.4 Distribution of the...

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