Lecture9ch5

Lecture9ch5 - STAT 350 LECTURE 9 Chapter 5(5.6 Describing...

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STAT 350 L ECTURE 9 Chapter 5 (5.6) Describing Sample Distributions Central Limit Theorem
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H OMEWORK #4 Chapter 5: 26, 30, 32, 34, 35(a)(c), 37, 42, 46
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A PPROXIMATE S AMPLING D ISTRIBUTION (E XAMPLE 5.14) The weight of 50 lb of rice from a certain producer has a normal distribution with μ =50 (lb), σ =2(lb) Suppose we draw 1000 random samples, and each sample is of size n=25 If we calculate the mean of each sample, how many sample means do we get? We can plot the histogram of these sample means See Figure 5.14 on page 224
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E XAMPLE 5.14
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S AMPLING D ISTRIBUTION Which values of the sample mean are more likely to occur? (48.5,51.5)
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S AMPLING D ISTRIBUTION Suppose we select a single sample of size 25 from a normal distribution with unknown μ and σ =2 If the sample mean is 50 for this sample: We can infer that the unknown mean μ (population mean) is almost certain to be in (48.5, 51.5) We can be reasonably confident that μ is (49, 51) Sampling distribution (of sample mean) make inferences about population parameter ( population mean μ )
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G ENERAL P ROPERTIES OF S AMPLING D ISTRIBUTIONS The sampling distribution of a statistic often tends to be centered at the value of the population parameter The spread of the sampling distributions of many statistics tend to grow smaller as the sample size n increases As the sample size increases, sampling distributions of many statistics become more and more bell- shaped (normal distribution)
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This note was uploaded on 04/23/2011 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture9ch5 - STAT 350 LECTURE 9 Chapter 5(5.6 Describing...

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