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Unformatted text preview: THE CENTRAL LIMIT THEOREM The World is Normal Theorem Sampling Distribution of x normally distributed population n=10 σ / √ 10 σ Population distribution: N( μ , σ ) Sampling distribution of x: N ( μ , σ / √ 10) Normal Populations ■ Important Fact: ★ If the population is normally distributed, then the sampling distribution of x is normally distributed for any sample size n. ■ Previous slide Nonnormal Populations ■ What can we say about the shape of the sampling distribution of x when the population from which the sample is selected is not normal? 53 490 102 72 35 21 26 17 8 10 2 3 1 1 100 200 300 400 500 600 Frequency Salary ($1,000's) Baseball Salaries The Central Limit Theorem (for the sample mean x) ■ If a random sample of n observations is selected from a population ( any population), then when n is sufficiently large, the sampling distribution of x will be approximately normal. (The larger the sample size, the better will be the normal approximation to the sampling distribution of x.) The Importance of the Central Limit Theorem ■ When we select simple random samples of size n, the sample means we find will vary from sample to sample. We can model the distribution of these sample means with a probability model that is , N n μ σ How Large Should n Be? ■ For the purpose of applying the central limit theorem, we will consider a sample size to be large when n > 30. Summary Population : mean μ ; stand dev. σ ; shape of population dist. is unknown; value of μ is unknown ; select random sample of size n ; Sampling distribution of x: mean μ ; stand. dev. σ / √ n; always true!...
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This note was uploaded on 02/13/2012 for the course BUS 350 taught by Professor Reiland during the Fall '08 term at N.C. State.
 Fall '08
 reiland
 Business

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