L20-09

# L20-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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11/19/09 Lecture 20 1 STOR 155 Introductory Statistics Lecture 20: Comparing two means Section 7.2 ( a modified case only ) The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

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11/19/09 Lecture 20 2 Comparing two population means Population 1: with mean s.d. Population 2: with mean s.d. Interested in the difference Sample 1: size mean s.d. Sample 2: size mean s.d. Consider the difference Assume the two samples are independent , and both and are large (e.g. at least 40). ö 1 ö 2 ö 1 à ö 2 D = X ö 1 à X ö 2 s 1 s 2 n 1 X ö 1 n 2 X ö 2 n 1 n 2 û 1 û 2
11/19/09 Lecture 20 3 Useful probability facts The random variable D has approximately a normal distribution with mean and standard deviation SD( D ) = An estimate of SD( D ) (Note: This is the only expression, not like in Lecture 19 with two different formulas) ö 1 à ö 2 û 2 1 =n 1 + û 2 2 =n 2 q SE D = s 2 1 =n 1 + s 2 2 =n 2 q

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11/19/09 Lecture 20 4 Confidence Interval for • Expression: where the margin of error – Confidence level C determines m = z ã SE D z ã [ D à m;D + m ] ö 1 à ö 2
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L20-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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