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Ni Nyoman Sulastri 11701373 STAT5023 Q1. M1 Rank M1 M2 Rank M2 M3 Rank M3 94.0 17.0 82.0 10.0 89.0 15.0 87.0 13.5 85.0 11.0 68.0 2.0 90.0 16.0 79.0 8.0 72.0 4.5 74.0 6.0 87.0 13.5 76.0 7.0 86.0 12.0 61.0 1.0 69.0 3.0 97.0 18.0 72.0 4.5 80.0 9.0 Total Rank 82.5 57.0 31.5 a)Hypotheses Ho : M1=M2=M3 (The median test scores are equal) Ha : At least two of the samples differ b)Significance level α=0.05 c)Critical value and rejection region X 0.05,2 2 =5.99 Reject the null hypothesis if H>5.99 d)Test statistic H= 1 S 2 [ ∑ i=1 k R i 2 n i − n ( n + 1) 2 4 ] S 2 = 1 n−1 [ ∑ i=1 k ∑ j=1 n i r ( X ij ) 2 − n ( n+ 1) 2 4 ] S 2 = 1 17 [ ( 289 +182.25+256 +36 +144+ 324+100 + 121+ 64 + 182.25+1+ 20.25+81 + 225+4 + 20.2 H= 1 28.44 [ ( 6806.25 6 + 3249 7 + 992.25 5 ) − 18 ( 19 ) 2 4 ] = 1 28.44 [ ( 1134.375+464.143 +198.45 )−162 e)Decision Since 6.06 ≥ 5.99 (0.025 < p-value < 0.05), we reject the null hypothesis 1

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Ni Nyoman Sulastri11701373STAT5023

Q1. M1Rank M1M2Rank M2M3Rank M3

94.017.082.010.089.015.0

87.013.585.011.068.02.0

90.016.079.08.072.04.5

74.06.087.013.576.07.0

86.012.061.01.069.03.0

97.018.072.04.5

80.09.0

Total Rank82.557.031.5

a) HypothesesHo:M1=M2=M3 (The median test scores are equal)Ha:At least two of the samples differb) Significance level=0.05c) Critical value and rejection region

Reject the null hypothesis if H>5.99d) Test statistic

e) DecisionSince 6.06 5.99 (0.025 < p-value < 0.05), we reject the null hypothesis

f) Pairwise comparisons

The result of pairwise comparisons using the equation above show in the table below

ComparisonTP-value

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