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tutorial06 - ISMT 111 BUSINESS STATISTICS TUTORIAL 6...

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1 ISMT 111 B USINESS S TATISTICS T UTORIAL 6 created by Andrew Yam Confidence Interval Estimation for Population Mean, µ § For large sample size n , if σ is unknown, use s instead For small sample size with normal population and known A ( 29 % 100 1 a - Confidence Interval for m is n z X s a 2 ± . § For small sample size and unknown from normal population A ( 29 % 100 1 a - Confidence Interval for m is n s t X n 2 ; 1 a - ± . § Notations: X : the point estimator of µ 2 a z : it corresponds to an area of 2 1 a - from the center of a standardized normal distribution (Note: 645 . 1 05 . 0 = z ; 96 . 1 025 . 0 = z ; 575 . 2 005 . 0 = z ) 2 ; 1 a - n t : it corresponds to an area of 2 1 a - from the center of a t distribution, with n 1 degree(s) of freedom (d.f.) a - 1 : Confidence Coefficient - measures the level of confidence that the C.I. will enclose the parameter we estimate. n / s : Standard Error of the Mean n s / : Estimated Standard Error of the Mean Confidence

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Assume X 1 and X 2 are independent populations; we have two samples drawn from X 1 and X 2 with sizes n 1 and n 2 respectively. § Interval Estimation with Large-Sample Size (for both n 1 and n 2 ) A ( 29 % 100 1 a - Confidence Interval for 2 1 m m - is 2 2 2 1 2 1 2 2 1 n n z X X s s a + ± - . Note: When 2 i s is unknown, use 2 i s instead. § Interval Estimation with Small-Sample Size and Unknown 2 i s (either one or both n i are small) Assumptions: - both populations of X 1 and X 2 are normal - common population variance, 2 2 2 2 1 s s s = = A ( 29 % 100 1 a - Confidence Interval for 2 1 m m - is 2 1 2 ; 2 2 1 1 1 2 1 n n s t X X p n n + ± - - + a . where s p is the pooled estimated standard deviation calculated as follows, ( 29 ( 29 2 1 1 2 1 2 2 2 2 1 1 - + - + - = n n s n s n s p Confidence Interval for Binomial Proportion p § For large sample size n A ( 29 % 100 1 a - Confidence Interval for p is n pq z p 2 ˆ a ± . § When
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This note was uploaded on 09/15/2008 for the course ISMT 111 taught by Professor Wanxuhu during the Fall '08 term at HKUST.

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tutorial06 - ISMT 111 BUSINESS STATISTICS TUTORIAL 6...

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