In a Kruskal-Wallis test for comparing three populations, the test statistic is calculated as H = 2.80. If the test is conducted at the 5% significance level, then:
A) the null hypothesis will be rejected
B) the null hypothesis will not be rejected
C) the alternative hypothesis will not be rejected
D) the test results are inconclusive
E) the t-test for matched pairs must be used

Question

Quizplus · Accepted Answer

The Kruskal-Wallis test is a non-parametric method for comparing three or more independent samples. It is used to determine if there are statistically significant differences between the groups' medians. The decision to reject or not reject the null hypothesis is based on the comparison of the calculated H value with the critical value from the Chi-square distribution (since the test statistic of the Kruskal-Wallis test follows a Chi-square distribution) at the given degrees of freedom (number of groups - 1) and the significance level (alpha). Without the critical value provided or the degrees of freedom, we cannot directly determine the outcome based on the H value alone. However, typically, an H value of 2.80 is considered low for rejecting the null hypothesis at a 5% significance level for most practical sample sizes and group numbers, implying that there is not enough evidence to suggest a significant difference between the groups. Therefore, the null hypothesis will not be rejected.

In a Kruskal-Wallis Test for Comparing Three Populations, the Test