Wek1PPT2304 - 1 ADM2304: M, N & R January 2012...

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Unformatted text preview: 1 ADM2304: M, N & R January 2012 Statistics for Management II DMS 1130 Section R: Mondays-19:00-22:00 Section N: Tue 16:00-17:30, Thu-14:30-16:00 Section M: Wed 13:00-14:30, Fri 11:30-13:00 Text Book: Business Statistics, Canadian Ed. Sharpe et al Prof.: Dr. Suren Phansalker Office : DMS 5142 Office Hours: Tue 14:00-15:30 2 Lecture#1 Sample Mean Distributions: t & Z Distributions Dr. Suren Phansalker Central Limit Theorem (CLT): As seen before, P-S. Laplace proved the main assertion of the CLT. However, in its modern form, it does have different forms. The following three major cases bring out the variations. Case I of CLT: If a large sample with size, n 30, is drawn from any much larger population X, of unknown distribution, then: But, and where , , and 2 are the population parameters. Then simply written: It sometimes is written as: ( 29 ) ( ), ( ~ 2 X X E N X = ) ( X E n X 2 2 ) ( = n N X 2 , ~ n N X , ~ 3 Case II of CLT: If the Population RV, X is itself Normally Distributed, then if is known, then for any sample size, (even n < 30): or Case III of CLT: If the Population RV, X is itself Normally Distributed, then if is unknown and must be estimated by s, the sample standard deviation, then: or Special Condition for Case III of CLT: If n, the sample size is fairly large (n 30 or n 120), then: or In other words, the t Distribution and Z Distribution become almost equal. n N X 2 , ~ - n s t X n 2 1 , ~ n N X , ~ - n s t X n , ~ 1 - n s N n s t X n 2 2 1 , , ~ - n s N n s t X n , , ~ 1 4 Some Examples of the CLT: Example 1 for Case I: A large sample of size 100 is taken from a population of marks on a...
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Wek1PPT2304 - 1 ADM2304: M, N & R January 2012...

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