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

211-01-2+Class+Notes+2-2 - DSC 211 CLASS NOTES 2-2 Page 1...

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DSC 211 CLASS NOTES 2-2 Page 1 COMPARING TWO or MORE POPULATIONS EXAMPLE Issue: Variability/consistency in service times for two bank tel ers. Teller-1* Teller-2* (There are 3 worksheets that are a part of class notes 2-2.) F-Test Suppose they had different training; we think tel er 1's training might be better. 7.2 10.9 SO FAR, IN CLASS NOTES 2-1: Bus Question: From our sample data, can we conclude that teller 1 is more consistent in 5.4 6 (1) COMPARING MEANS (MU'S): service time than teller 2? 3.7 6.7 Data: We recorded the service time (min) for 100 random customers for ea of the 2 tel ers. Sample Std Devs 6.4 8.3 (Required condition: Populations are approximately Normal) Calculations with Excel: We believe that the two populations of times are approximately Normal. minutes 11.2 14.3 Test Stat: Analysis: F-Test minutes 8.7 3.7 [ s1^2/n1 + s2^2/n2 ] ^.5 df = t-test: 2 sample assuming unequal variances 1. Hypotheses: Ho: var1/var2 >= 1 var1 >= var2 9.3 7.6 Ha: var1/var2 < 1 var1 < var2 6.9 8 (Required condition: Differences are approximately Normal) 2. Test Statistic: 9.1 8.1 Test Stat: =TINV and =TDIST, or 3. Sig Level: alpha = .05 8.6 1.3 s(D) / n^.5 df = n -1 t-test: paired 2 sample for means 4. Reject Rule: Reject Ho if F < value of F that only 5% are below Why smal F -- and not large F?? 7.3 10.6 (2) COMPARING PROPORTIONS (P'S): Reject Ho if F < 6.1 8 5. Calculations: Data set in columns L and M: Observations in minutes per service transaction 6.7 10.8 4.4 10.5 Test Stat: =NORMINV and =NORMDIST 7.4 9.7 F = 7.6 3.6 p-value = 8.9 7.3 NOW THREE MORE SITUATIONS: 6. Conclusion: For turn-in, 10.9 7.8 (3) COMPARING THE VARIATION or SPREAD or CONSISTENCY of two populations -- ARE THEY DIFFERENT? Bus Answer: print this 7.2 4.4 box 4.2 4 10.5 7.9 BusQues: Is the variation (are the variances or stdevs) different? --- 9.3 12.5 1. Hyp: s1^2 = 10.3 s2^2 = 39.2 8.2 6.2 NOTE --Can use the excel tool below for steps 4 and 5 of analysis: 5.8 10.3 2. TestStat: Req Condition: Populations are approx Normal. (The tool is set up for one-sided tests only.) 7.2 8 F-Test Two-Sample for Variances 7 4.3 NOTE: If Ho is true, the ratio should NOT BE TOO DIFFERENT than one. 6.1 10.4 Tel er-1* Tel er-2* 9.1 7.6 Mean 7.91 7.84 8.1 11.3 Variance 3.35 10.95 9.4 6.5 Observations 100 100 8.4 13.4 3. Sig Level: alpha = .05 df 99 99 10.1 10 4. Reject Reject Ho if F < smal less than 1 value or F > large greater than 1 value F 0.306 8.1 3.5 Rule: smal value seen .025 or less = 0.207 =FINV(.975,7,9) Note: first argument is prob above. P(F<=f) one-tail 0.000 5.6 6.5 large value seen .025 or less = 4.197 =FINV(.025,7,9) F Critical one-tail 0.717 6.2 9 Reject Ho if F < 0.207 or F > 4.197 7.3 10.6 5. Calc's: Data Set: samples from population (1) and population (2) Ave(x-bar) StDev 9.9 5.9 (1) 7 4 9 12 8 6 9 14 8.6 3.2 5.9 14.5 (2) 10 7 13 18 4 8 21 20 5 8 11.4 6.3 8.1 4.7 s1^2 = 10.27 8.4 2.2 s2^2 = 39.16 7.3 7.1 F = 0.262 7.7 5.3 p-value = 0.091 9.1 4.1 8.4 5.2 6. Concl's: Do not reject Ho. 7.8
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211-01-2+Class+Notes+2-2 - DSC 211 CLASS NOTES 2-2 Page 1...

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