Question

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
51 81 61
67 94 44
74 92 31
42 85 52
64 91 55
Use the Kruskal-Wallis test and = 0.05 to determine whether there is a significant difference among the ratings for the products.
a)H0: All populations of product ratings are identical.
Ha: Not all populations of product ratings are identical


Find the value of the test statistic.

Answer 1

1. The value of the test statistic is equal to 9.98.
2. There's sufficient statistical evidence at a 5% level of significance to state that there's a significant difference among the ratings for the products A, B, and C.

What is Kruskal-Wallis test?

The Kruskal-Wallis test is also referred to as one-way ANOVA on ranks or Kruskal-Wallis H test and it can be defined as a rank-based nonparametric test that is typically used to determine whether or not there are statistically significant differences between two (2) or more samples of an independent variable on either a continuous or ordinal dependent variable.

This ultimately implies that, a Kruskal-Wallis test can be used to determine whether two (2) or more samples originate from the same distribution.

Based on the given sample, the hypothesis is given by:

• H₀: Ratings are the same for all the three products.

• Ha: There are differences among the ratings for the products.

For this exercise, we would use R-studio to perform the Kruskal-Wallis test as follows:

df₁ = read.table (header = TRUE, text ="

product   Ratings

    A           55

    A           64

    A           79

    A           41

    A           69

    B           85

    B           99

    B           91

    B           88

    B           95

    C           65

    C           49

    C           35

    C           51

    C           58

")

DF₁ kruskal.test(Ratings ~ product, data = df1)

Based on the Kruskal-Wallis test, we obtained the following results (outputs):

Kruskal-Wallis chi-squared = 9.98.

Degrees of freedom, DF = 2.

P-value = 0.006806.

Next, we would determine the test statistic as follows:

Test statistic = Kruskal-Wallis chi-squared = 9.98.

P-value = 0.007.

Therefore, the p-value (0.007) is less than α = 0.05. Based on this, we should reject the null hypothesis (H₀) and accept the alternate hypothesis (Ha).

In conclusion, we can infer and logically deduce that there's sufficient statistical evidence at a 5% level of significance to state that there's a significant difference among the ratings for the products A, B, and C.

Read more on null hypothesis here: brainly.com/question/14913351

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