To determine whether four population means are equal, a sample from each population was selected at random. Using the Kruskal-Wallis test, H was computed to be 2.09. What is our decision at the 0.05 level of risk? A) Fail to reject the null hypothesis because 0.05 critical value of 1.96

Question

To determine whether four population means are equal, a sample from each population was selected at random. Using the Kruskal-Wallis test, H was computed to be 2.09. What is our decision at the 0.05 level of risk? A) Fail to reject the null hypothesis because 0.05 < 2.09 B) Fail to reject the null hypothesis because 2.09 < 7.815 C) Reject the null hypothesis because 7.815 is > 2.09 D) Reject the null hypothesis because 2.09 > critical value of 1.96

Quizplus · Accepted Answer

To make a decision using the Kruskal-Wallis test, we compare the calculated test statistic (H) with the critical value of the chi-square distribution with degrees of freedom equal to the number of samples minus one (k-1), where k is the number of populations being compared.

For this problem, we have k=4 populations, so k-1=3 degrees of freedom. At the 0.05 level of significance, the critical value of chi-square with 3 degrees of freedom is 7.815.

Since the calculated test statistic value (H=2.09) is less than the critical value (7.815), we fail to reject the null hypothesis that the population means are equal. Therefore, the answer is B.

To Determine Whether Four Population Means Are Equal, a Sample