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Unformatted text preview: ISE426/526 Solutions  Assignment 2 Document Name: Assignment 2 Solutions Release Date: June 20, 2007 (Wednesday) 1 – a: Since, this problem builds on from problem 1 of homework assignment 1 ; we will use the results from that assignment, without recalculating any parameter. Type of Root Stock Length (centimeters) 1 2 3 4 5 6 7 8 . i y . i y Type I 2569 2928 2865 3844 3027 2336 3211 3037 23817 2977.125 Type II 2074 2885 3378 3906 2782 3018 3383 3447 24873 3109.125 Type III 2505 2315 2667 2390 3021 3085 3308 3231 22522 2815.250 Type IV 3849 3925 3539 3943 3677 3566 3601 3291 29391 3673.875 Type V 1532 2552 3083 2330 2079 3366 2416 3100 20458 2557.250 = .. y 121061 .. y = 3026.525 In the previous assignment, it was established that at least one of type of root –stocks differs significantly from the rest. We are required to determine this, using Tukey’s test. ANOVA table: Source of variation Sum of Squares Degrees of Freedom Mean Square Fo Between Treatment 5545450 = Treatments SS a 1 = 4 5 . 1386362 = Treatments MS E Treatment o MS MS F = = 6.433 Within Treatment 7542858 = E SS Na = 35 23 . 215510 = E MS Total 13088308 = T SS N1 = 39 Page 1 of 20 ISE426/526 Solutions  Assignment 2 Recall, for multiple comparison tests such as Tukey’s test, the hypotheses are set as follows: For all , j i ≠ j i H μ μ = : j i H μ μ ≠ : 1 Part 1 – Solution by manual computation Tukey’s test statistic: n MS f a q T E ) , ( α α = a = number of treatments = 5, f = degrees of freedom for error = 35 ) , ( f a q α = ) 35 , 5 ( 05 . q = 4.066 3541 . 667 8 23 . 215510 066 . 4 = = α T Decision Rule: Reject Ho, if  . .  j i y y T < α Comparison  . .  j i y y α T Decision Conclusion Type I and II 132 667.354 Do not reject Ho Not significantly different Type I and III 161.875 667.354 Do not reject Ho Not significantly different Type I and IV 696.75 667.354 Reject Ho I and IV are different Type I and V 419.875 667.354 Do not reject Ho Not significantly different Type II and III 293.875 667.354 Do not reject Ho Not significantly different Type II and IV 564.75 667.354 Do not reject Ho Not significantly different Type II and V 551.875 667.354 Do not reject Ho Not significantly different Type III and IV 858.625 667.354 Reject Ho III and IV are different Type III and V 258 667.354 Do not reject Ho Not significantly different Type IV and V 1116.625 667.354 Reject Ho IV and V are different From the analysis, it is clear that Type IV differs from Types I, III and V. Type IV is not significantly different from Type II. Types I, II, III and V are not significantly different from each other....
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This note was uploaded on 11/22/2009 for the course ISE 526 taught by Professor Farrington during the Summer '07 term at University of Alabama  Huntsville.
 Summer '07
 Farrington

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