211-01-2+Class+Notes+2-1

211-01-2+Class+Notes+2-1 - DSC 211 REVIEW MOD 1: CLASS...

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DSC 211 CLASS NOTES 2-1, page 1 Comparing Two Populations REVIEW Target Population: e.g., Customer Incomes (X) MOD 1: Questions (1 or 2-sided) about: across k categories Analysis: 6 Step Hypothesis Testing "Conclusion About Specific Question (one- or two-sided) the Claim" 1 Ho & Ha --> Ha is same as the question IN SHORT: 2 Test Stat Is sample Sample evidence inconclusive. Cannot conclude (Ha) 3 Alpha = usually 0.05 inconsistent 4 Reject Rule --> Use TINV, CHIINV, NORMINV with Ho ? Reject rule is consistent with Ha. If so, then 5 Calculate the Test Stat (from the sample results) "yes" to NOW: Part 2 of our DSC 211 Course p-value --> Use TDIST, CHIDIST, NORMDIST bus question. Comparing 2 or more Populations 6 Reject Ho or Do not reject Ho Issue: Population 1 Data: Assembly Plant 1 Assembly Times Plant 2 Assembly Times Times at 2 Plants BQues: Question (another way to state it): Do the sample results provide evidence that the averages are different? 1 2 because we know its distribution (2) If Ho is true: t distribution with df we can calculate with df = 3 alpha = .05 4 Reject Ho if t < (low neg value) or t > (high pos value) --2-sided Hyp Use =TINV(.05,df) 5 from the two sample results calculate these 1st four values df = use formula above to calc df t= use formula above to calc t p-value= use TDIST with the t and df just calculated Sample (n) --> Test Statistic : t-Test for Mean, t = (x-bar - mu o ) / (s/n^.5) μ - average income & some value, mu o ChiSq Test for Variance, ChiSq = (n-1)*s^2/var o σ 2 or var - variability of incomes & a value, var o Normal Test for Prop, p-bar with stdev = (p o *(1-p o )/n)^.5 p - proportion of incomes > some value, p o ChiSq Goodness of Fit Test, ChiSq = Sum of (f-e)^2/e p1,p2,p3, . .. - distribution of incomes First -- comparing means ( μ 's) x-bar 1 x-bar 2 Sample from 1 (n 1 ) s 1 ^2 Sample from 2 (n 2 ) s 2 ^2 μ 1 - ave time μ 2 - ave time Common question, "Are the assembly times different?" Which usually means --> Are μ 1 and 2 different? (Or, Do μ 1 and μ 2 differ by more or less than D?) (Ques could be Is μ 1 greater than μ 2 ?) Ho: μ 1 = μ 2 , (or, μ 1 - μ 2 = D, where D=0 in this case) Ha: μ 1 <> μ 2 , Test Statistic. (1) t = [(x-bar 1 -x-bar 2 ) - 0] ( (s 1 2 /n 1 + s 2 2 /n 2 )^0.5 (s 1 ^2/n 1 + s 2 ^2/n 2 )^2 (s 1 ^2/n 1 )^2/(n 1 -1) + (s 2 ^2/n 2 )^2/(n 2 -1) x-bar 1 = x-bar 2 = s 1 ^2= s 2 ^2=
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can (cannot) conclude . . . 6 Reject or Do Not Reject Ho. NOTE: We will do calculations manually with the following example. However, in practice we will use excel's tool: Example: Issue: Two possible methods of assembly for new product. Two Sample t -Test--> Unequal Variances Question: From data gathered using the two methods, can we conclude that the avg assembly times differ? [If so, how?] Data: Samples of 25 randomly selected workers; recorded assembly times for each. May not be explicit. 6.29 min 6.02 min Diff = 0.27 What do you think about bus question 1. Hypotheses: just looking at x-bars -- before Analysis?
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211-01-2+Class+Notes+2-1 - DSC 211 REVIEW MOD 1: CLASS...

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