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Unformatted text preview: 1 ADM2304: M, N & R January 2012 Statistics for Management II DMS 1130 Section R: Mondays19:0022:00 Section N: Tue 16:0017:30, Thu14:3016:00 Section M: Wed 13:0014:30, Fri 11:3013:00 Text Book: Business Statistics, Canadian Ed. Sharpe et al Prof.: Dr. Suren Phansalker Office : DMS 5142 Office Hours: Tue 14:0015:30 2 Lecture#1 Sample Mean Distributions: t & Z Distributions Dr. Suren Phansalker Central Limit Theorem (CLT): As seen before, PS. 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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 Winter '11
 Phansalker

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