Question

# A sample of 15 consumers provided the following product ratings for three different products. Five consumers...

A sample of 15 consumers provided the following product ratings for three different products. Five consumers were randomly assigned to test and rate each product.

Product
A B C
58 88 68
61 97 47
77 96 38
46 89 56
67 98 59

Use the Kruskal-Wallis test and α = 0.05 to determine whether there is a significant difference among the ratings for the products.

a) Find the value of the test statistic.

b) Find the p-value. (Round your answer to three decimal places.)

p-value =

 Type score Rank A 58 5 A 61 7 A 77 10 A 46 2 A 67 8 B 88 11 B 97 14 B 96 13 B 89 12 B 98 15 C 68 9 C 47 3 C 38 1 C 56 4 C 59 6
 sample size ni sum of ranks ∑Ri (∑Ri)2/ni A 5 32 204.80 B 5 65 845.00 C 5 23 105.80 total N = 15 total = ∑(∑Ri)2/ni = 1155.60 test stast:H= =(12/(N*(N+1)))*∑(∑Ri)2/ni )-3*(N+1)= 9.780

a)

value of the test statistic =9.78

b)

p value =0.008

reject null hypothesis since p value <0.05

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