Q2. MANNWHITNEY As part of a product-testing program, a paint manufacturer painted 12 houses in a suburban community. Six of the houses were painted with the company’s own product, and the other 6...

Q2. MANNWHITNEY

As part of a product-testing program, a paint manufacturer painted 12 houses in a
suburban community. Six of the houses were painted with the company’s own
product, and the other 6 were painted with a competitor’s paint. After 5 years, a panel
of homeowners inspected the 12 houses and ranked them according to how well the
paint was holding up. The rankings are as follows:
Company’s paint 1 3 4 5 7 8
Competitor paint 2 6 9 10 11 12
Do these data indicate a significant difference between two brands of paint? Test at a
=.05

IN PICTURE I HAVE ATTACHED EXAMPLE Q AND SOLUTION THAT NEED TO BE FOLLOWED TO DO THIS QUESTION. THANK YOU

Extracted text: 1. The size of leaves taken from bramble bushes were measured to see if there is a difference between the size of the leaves growing in full sunlight and those growing in the shade. Test the hypothesis using 0.05 level of significance. Width Of Leaf / Cm Sunlight 6.0 4.8 5.1 5.5 4.1 5.3 4.5 5.1 Shade 6.5 5.5 6.3 7.2 6.8 5.5 5.9 5.5 STEP1 Ho: There is no difference between the two treatments. Therefore, there is no tendency for the ranks in sunlight condition to be systematically higher (or lower) than the ranks in the shade condition. H1: There is a difference between the two treatments. Therefore, the ranks in sunlight condition are systematically higher (or lower) than the ranks in the shade condition. Sunlight RA Shade RB 6.0 12 6.5 14 STEP 2 4.8 3 5.5 8.5 5.1 4.5 6.3 13 5.5 8.5 7.2 16 4.1 1 6.8 15 5.3 5.5 8.5 4.5 2 5.9 11 5.1 4.5 5.5 8.5 ERA = 41.5 ERB = 94.5 a = .05 UA= NANB + [nA(nA+1)] /2 – ERA = 8(8) + [8(8+1)] /2 – 41.5 nA = 8 = 58.5 UB = nAnB + [nB(nB+1)] / 2 – ERB nB = 8 8(8) + [8(8+1)]/2 – 94.5 = 5.5 | Ucritical = 13 STEP 4 STEP 3 U min (UA, The original scores were ranked ordered and a Mann-Whitney U Test was used to compare the UB) ranks for the n 8 in sunlight condition and the n 8 in shade condition. The results indicate = 5.5 significant difference between the two conditions, U = 5.5, with the sum of ranks equal to 41.5 5.5 < 13="" for="" sunlight="" condition="" and="" 94.5="" for="" shade="" condition.="" therefore,="" the="" null="" hypothesis="" is="" rejected.="" step="" 5="" step="">


Extracted text: BHPY2044 STATISTICAL TECHNIQUES FOR PSYCHOLOGY II Critical Values of the Mann-Whitney U for a = .05* .05 (lightface type) and for a iwo-tailed test al a = the obtained U must be cqual to or less than the critical value in the .05 (boldface *Critical values arc provided for a one-tailed test al a = and n, type) To be significant for any given n, Lable, Dashes (-) in the body of the table indicate that no decision is possible at the stated level of significance and values of n, and 6 7 8. 10 11 12 13 14 15 16 17 18 19 20 1 2 4 5 1 1 2 2 2 3 4 4 4 1 2 2 1. 1 6. 1 2 3. 4 5 7 7 9. 10 11 3 1 2 2 3 4 5 7 7 9 10 11 12 14 15 16 17 18 6. 4 1 2 3 4 5 7 1 2 3 4 7 .10 11 11 12 13 13 4 5 11 12 13 15 16 18 19 20 22 23 25 1 1 3 5 7 11 12 13 14 15 17 18 19 20 28 24 25 26 30 32 23 19 6. 3 7 10 12 14 16 17 19 21 3 6 8. 10 11 13 14 16 17 21 22 25 27 11 13 15 17 19 21 24 26 28 30 33 35 37 39 7 2 4 5 6 10 12 14 16 18 20 22 24 26 28 30 32 34 3 5 10 13 15 18 20 23 26 28 31 33 36 39 41 44 47 3 8 10 13 15 17 19 22 24 26 29 31 34 36 38 41 2 9. 15 18 21 24 27 30 33 36 39 42 45 48 51 54 12 6. 7 9 3 10 12 15 17 20 23 26 28 31 34 37 39 42 45 48 11 14 17 20 24 27 31 34 37 41 44 48 51 55 58 62 10 4 7 11 14 17 20 23 26 29 33. 36 39 42 45 48 52 55 3 61 65 58 12 16 19 23 27 31 34 38 42 46 50 54 57 69 11 1 13 16 19 23 26 30 33 37 40 44 47 51 55 62 3 5 9. 13 17 21 26 30 34 38 42 47 51 55 60 64 68 72 77 12 4 7 11 14 18 22 26 29 33 37 41 45 49 53 57 61 65 69 1 10 15 19 24 28 33 37 42 47 51 56 61 65 79 75 80 84 13 2. 8. 12 16 20 24 28 33 37 41 45 50 54 59 63 67 72 76 1 51 77 82 74 87 92 83 7 11 16 21 26 31 36 41 46 56 61 66 71 14 13 17 22 26 31 36 40 45. 50 55 59 64 67 78 1 18 23 28 33 39 44 50 55 61 66 72 77 83 88 94 100 15 3 7 12 10 14 19 24 29 34 39 44 49 54 59 64 70 75 80 85 90 1 95 86 14 19 25 30 36 42 48 54 60 65 71 77 83 89 101 107 16 3 6 11 15 21 26 31 37 42 47 53 59 64 70 75 81 92 98 1 15 20 26 33 39 45 51 57 64 70 77 83 89 96 102 109 115 17 3 11 17 22 28 34 39 45 51 57 63 67 75 81 87 93 99 105 75 82 88 95 102 109 116 123 68 61 41 48 55 61 35 30 18 4 9. 16 22 28 12 18 24 36 42 48 55 67 74 80 86 93 99 106 112 2 7 109 116 99 106 72 80 87 94 101 123 130 58 52 19 4 10 17 23 30 37 44 51 65 13 19 25 32 38 45 58 65 72 78 85 92 113 119 7 84 92 100 107 115 123 130 138 69 62 20 4 11 18 25 32 39 47 54 62 77 13 20 27 34 41 48 55 69 76 83 90 98 105 112 119 127 44 649 3. 64 96