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Unformatted text preview: 10.3 Comparing Two Population Means Def’n: Two samples drawn from two populations are independent if the selection of one sample from one population does not affect the selection of the second sample from the second population. Otherwise, the samples are dependent . Notation: Two samples require appropriate subscripts. e.g. μ 1 and μ 2 , n 1 and n 2 Assumptions : 1. The two samples are independent. 2. The standard deviations σ 1 and σ 2 of the two populations are unknown but assumed to be equal, that is σ 1 = σ 2 . 3. 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. Checking the Assumptions : The last assumption can be “checked” just like in Ch. 9. The first assumption can be “checked” by analyzing the experimental design. The second, however, can use “math”. Æ “rule of thumb” about Assumption #2: “okay” if ratio of s max / s min < 2. Hypotheses : Although there are two population means (a.k.a. parameters) in our data structure, we consider them together as ONE parameter: μ 1 – μ 2 . Thus, we have H : 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....
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- Winter '07
- Normal Distribution, test statistic t0