In a Kruskal-Wallis test, there are four samples and the value of the test statistic is calculated as H = 8.79. Under these conditions, which of the following is the most accurate statement that can be made about the p-value?
A) It is greater than 0.10.
B) It is greater than 0.05 but smaller than 0.10.
C) It is greater than 0.05.
D) It is greater than 0.025 but smaller than 0.05.

Question

Quizplus · Accepted Answer

To determine the p-value, we need to compare the calculated H value to the critical values of the chi-squared distribution with degrees of freedom equal to the number of samples minus one (k-1). For this problem, we have k = 4 samples, so degrees of freedom = 4-1 = 3. Using a chi-squared distribution table, we find that the critical value for a significance level of 0.05 and degrees of freedom = 3 is 7.815. Since our calculated H value (8.79) is greater than the critical value, we can reject the null hypothesis and conclude that there is a significant difference between at least two of the samples. The p-value for this test is the probability of obtaining an H value greater than or equal to 8.79, given that the null hypothesis is true. This probability is between 0.025 and 0.05, so the most accurate statement about the p-value is that it is greater than 0.025 but smaller than 0.05, which corresponds to answer choice D.

In a Kruskal-Wallis Test, There Are Four Samples and the Value