UASTAT141Ch24-25

UASTAT141Ch24-25 - Ch 24 Comparing Two Population Means...

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Ch. 24 - Comparing Two Population Means Assumptions : 1. The two samples are independent. 2. At least one of the following is also true: i. Both samples are large (i.e. n 1 30 and n 2 30) ii. If either one or both sample sizes are small, then both populations from which the samples are drawn are normally distributed. 3. (Optional) The standard deviations σ 1 and σ 2 of the two populations are unknown and unequal to each other; that is, σ 1 σ 2 . Checking the Assumptions : The first assumption can be “checked” by analyzing the experimental design. The 2 nd assumption can be “checked” just like in Ch. 23. The third, however, requires a formal test that is highly sensitive. Hypotheses : As in Ch. 22, there are two population means (a.k.a. parameters) in our data structure and we consider them together as ONE parameter: μ 1 μ 2 . Thus, we have H 0 : μ 1 μ 2 = 0 H A : μ 1 μ 2 0 Note that we could use any value to compare to, but zero has a ‘special’ interpretation. Also, tests can be one-sided, too.

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This note was uploaded on 07/31/2011 for the course STAT 141 taught by Professor Paulcartledge during the Winter '10 term at University of Alberta.

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UASTAT141Ch24-25 - Ch 24 Comparing Two Population Means...

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