Nonparametric Hypothesis Test

Using the research question and data below conduct a equivalent nonparametric test of hypothesis below.

The hypothesis for the ANOVA test is:

H0: μ1=μ2=μ3=μ4=μ5=μ6=μ7=μ8=μ9 (all means are equal)
H1: Not all means are equal (at least one is different)

Telecommunication Services Materials Information Technology Industrials Health Care Financials Energy Consumer Staples Consumer Discretionary
2,558.83 4,372.00 10,017.85 2,310.94 3,975.79 35,383.81 4,382.37 2,721.77 5,012.00
3,935.32 8,848.44 4,430.00 5,552.00 32,642.89 5,316.00 2,077.45 6,678.96 24,340.41
58,465.20 20,986.61 6,656.64 15,219.00 16,911.67 29,168.98 27,948.65 3,887.22 26,466.01
7,954.27 19,403.61 13,853.50 30,589.94 5,913.40 24,713.46 2,437.26 13,583.42 52,693.95
40,639.73 2,966.58 16,644.20 2,902.37 17,818.00 17,321.00 3,650.71 16,057.42 43,649.22
61,724.00 2,147.10 3,658.85 4,083.37 22,036.45 2,103.82 4,689.07 46,798.98 30,333.24
4,115.39 5,905.68 23,231.24 8,511.26 2,378.10 15,652.60 3,443.05 10,561.00 1,269.00
19,777.66 6,502.30 742 606 24,821.78 16,450.00 6,286.40 16,864.29
7,771.12 5,503.58 679.634 5,742.36 4,578.55 6,689.38 3,514.19 26,702.62
3,859.10 10,334.00 5,374.27 7,262.86 16,671.12 8,014.44 2,337.52 7,071.32
17,891.01 7,902.02 18,327.26 25,911.73 14,512.45 2,395.12 7,117.18
2,892.93 744 5,674.09 5,285.63 23,453.23 5,226.85 11,205.41
6,601.13 3,484.00 2,552.50 19,922.59 55,785.00 7,806.55
2,123.89 3,484.00 687.061 4,532.02 33,471.00 15,595.78
3,148.84 5,184.00 10,464.03 22,314.00 3,049.89
6,072.79 4,682.00 6,437.70 29,484.42 3,204.92
6,065.13 5,642.41 9,399.43 10,587.78
2,282.24 4,975.00 44,668.00
10,773.72 10,609.73
2,997.83 1,625.12
2,193.48 4,444.52
3,157.53 14,650.83
27,809.59 2,300.50
12,572.22 2,964.42
34,602.82 7,577.23
6,149.22 -7,639.09
6,361.46
3,909.99
Anova: Single Factor

SUMMARY
Groups Count Sum Average Variance
Telecommunication Services 28 368406.433 13157.373 275132209.153
Materials 16 112449.917 7028.120 32516735.240
Information Technology 14 112529.086 8037.792 52830787.805
Industrials 10 82780.089 8278.009 77989255.564
Health Care 7 101676.306 14525.187 122368775.237
Financials 26 295435.496 11362.904 106123998.392
Energy 18 312869.917 17381.662 249582632.914
Consumer Staples 12 120048.842 10004.070 154597123.880
Consumer Discretionary 17 292969.574 17233.504 220765877.459

ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1877651080.516 8.000 234706385.064 1.472 0.173 2.006
Within Groups 22168063990.048 139.000 159482474.749

Total 24045715070.563 147.000