Question

In: Statistics and Probability

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
53 83 63
60 99 49
79 91 33
41 82 51
69 93 52

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

State the null and alternative hypotheses.

H0: MedianA = MedianB = MedianC
Ha: MedianA < MedianB > MedianCH0: MedianA = MedianB = MedianC
Ha: MedianA ≠ MedianB ≠ MedianC    H0: Not all populations of product ratings are identical.
Ha: All populations of product ratings are identical.H0: All populations of product ratings are identical.
Ha: Not all populations of product ratings are identical.H0: MedianA ≠ MedianB ≠ MedianC
Ha: MedianA = MedianB = MedianC

Find the value of the test statistic.

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

p-value =

State your conclusion.

Reject H0. There is not sufficient evidence to conclude that there is a significant difference among the ratings for the products.Do not reject H0. There is sufficient evidence to conclude that there is a significant difference among the ratings for the products.    Do not reject H0. There is not sufficient evidence to conclude that there is a significant difference among the ratings for the products.Reject H0. There is sufficient evidence to conclude that there is a significant difference among the ratings for the products.

Solutions

Expert Solution

Kruskal-Wallis test steps

Based on test done above following are answers to all parts:

The null and alternative hypotheses:

Correction answer is:

H0: All populations of product ratings are identical

Ha: Not all populations of product ratings are identical

Test Statistics: 10.22

p-value = 0.006

Since p = 0.006 < 0.05, Reject null hypothesis H0. There is sufficient evidence to conclude that there is a significant difference among the ratings for the products.

orchestra answered 2 years ago
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