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# lecture9ccle - CHAPTER 4.2 INFERENCE THE C O N F I D E N C...

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I N F E R E N C E - T H E C O N F I D E N C E I N T E R VA L CHAPTER 4.2

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RECALL: A HISTOGRAM OF 10,000 SAMPLE MEANS EVERY SAMPLE IS SIZE 100 AND THE MEAN OF ALL SAMPLE MEANS IS CLOSE TO MU 94.51919

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THE SAMPLING DISTRIBUTION IS NEARLY NORMAL BASED ON ONLY 10,000 SAMPLES, A FRACTION OF WHAT THEORY DEMANDS
L I M I TAT I O N S 10000 repetitions of a small samples is not the same as infinite. While it looks pretty good, we need more. So we rely on the CENTRAL LIMIT THEOREM The Central Limit Theorem has some conditions, when met, tell us that our sampling distribution will approximate a normal distribution with mean= μ and a standard deviation which is equal to the standard error:

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T H E C E N T R A L L I M I T T H E O R E M THE THEORY
T H E K E Y P O I N T The Central Limit Theorem tells us that if we collect one random sample from a population, and if the sample is large ( 30) and if the population size is much larger (at least 10 times) than the sample size and not strongly skewed, then the sampling distribution is NORMAL with mean= μ and a standard deviation which is equal to the standard error:

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A N A P P L I C AT I O N O F T H E T H E O RY So Chapter 4.2 is trying to say is “suppose we don’t
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