Question

The following statistics are calculated by sampling from four normal populations whose variances are equal: (You may find it useful to reference the t table and the gtable.) X1 163, ni = 5; 2 = 171, n2 = 5; J3 = 166, n3 = 5; X4 = 158, n4 = 5; MSE = 41.2 a. Use Fisher's LSD method to determine which population means differ at a = 0.05. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) Population Mean Differences Can we conclude that the Confidence Interval population means differ? 1No H12 1No H1 3 1 No 1 No H2 3 1No H2 4 1No H3 4 b. Use Tukey's HSD method to determine which population means differ at a 0.05. (If the exact value for nT- cis not found in the table, then round down. Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) Population Mean Differences Can we conclude that the Confidence Interval population means differ? No μ1-μ2 No μ1- μ3 No μ1-μ4 No μ2-μ3 No 2-H4 No μ3-μ4

Answer 1

Solution fsm given datas n 5 x,163 n25 MSE u2 Critical Value of t a:oos 20- - sota M SC 2-199 2.1199 9.19 4 OS5 - 8-60s 86 Lso 8.61 Now' hove to ind ou he Confedence dnevval : wet

for 98 F(l- laimit (-8 86) -16.6 pen imit (- 8 Conclusion Since Conidence Jnlenval Contelns zeno So uwe Conetude Can not that differ Population MODns t LSD 19.8 (99$91) (-31 ± 86 oukn dimit -3-8.6)

4pen imit (198+2- 5.61 -HA, 54) Conctusion Confidence dntnval Contains eo Since cannot Conclude differ that pulaion Mans M-Hu ( 63- IS8) t 8-613 - 58.6 loa limit (5-8.61) 19.2 uppn limit (s+961) 713.61 (~3.61, 13.61) Conctusion Since Condnce dnfna conkins Zno Conclude Cam noi So we hat differ Apulation Means

LSD 9.8 FS own limit 5-8.61 3.6 uppnlinit (S+8.61) こ13.61 fo (H2- Conf:dence nltrvl -> 3.61 1361 Conclusion Since (onfdente dnterval Contains geo Cannot conelude Sa ue Hhas Aapulation d?ffer Muans for M2-Mu 2- ( !9.8 F(85t It. 198 干£1

UPpe 3+8.61) 21.61 tor (2 Conkt dence dntenl 3 (439,2161 Conclusion & Cockidtnce ^ntera does nol Contain 3eno Since Se Can Conclude tha Populaian Muans for M3- My 198 (851- 91 8+ 86 lou linit (8-8.61) uppen imi 18+8.61 tor (M3- My) contidence n tevual - C19.9110-) Conclusion since Cone?dence dmterval Contains we cannot- so The paeusation Conclude Meams

V4.05 0-4 91 P h 7 So, TUKey's HsD wi be MSE 41-2 4.05 2 5 5 4.Us 206 (o 2 +0.2) 4.0S 20 6 *Or -4.os .24 4.0S 2 871 HSD 6275 for M M (- 2) HSD - -8 t625 loelimit (-8-6275) -19.6275 uppen im - 627

for (A ) 6275, 3.6275 Concdusion Centains 3eno so Snce Confidence daterval e Cannol conchde dffen that Apulation Means for MI-M3' (7 - HsD St29 191-91) -3 6215 3-6275 -I4.6235 ufpes limit -3 1.627S 8.6215 (-4.6275, 8.62 75) fo Mi - Condence infenval > Conclusion Conkidene dnterval (ontains Since 2evo so we Caneiol Ganeiude dffer population Meams

MI-AMu (63- IS8 .62 F5 5 62 75 Lirmit (s-625) -6 629S upperlimit S L6275) 627S (-6.6275, 16. 6275) M, -M Confidence Jntervel -> Conclusion Sine Confidme dnktrval Contains zero so we Conehude Cannol haf oputaon Mcans 2-M3 lounimit 17i-66) 6275

5- H625 t limit -6 6275 uppen limil +HSD - S+ 6235 16.6215 uppe limit (-6 Confidince dntenul - 625, 16.6275) Conelusion oalidroeintrve! (ontains evo Since So we Cannot conclude that populeion Means N2-Mu NL-M HSD (r31- is8) t 62S 13 625 lower limit 2.6225

10 uppn limi 1362s 2 46275 (2 625, 24.627s) Conclusion Confidinte Jntervd does nol contain 3e1o so ux Since Can Conclude Means dffe poputation M3-My M3-MM HSO 8 Il62 S louwe limit (St. 29.11-8) - 3. 6275 uppen imit : (81 275) . 424S dntey vas Canf:demie M3- My 1,62 5 usiono Confidene dnterval Sine Contains 3evo e cam not Conelude thal Populchion