In a Friedman test for comparing four populations, provided that there as eight blocks, the test statistic is calculated as = 10.98. If the test is conducted at the 5% significance level, the conclusion and p-value will be: A) reject the null hypothesis, and 0.01

Question

In a Friedman test for comparing four populations, provided that there as eight blocks, the test statistic is calculated as  = 10.98. If the test is conducted at the 5% significance level, the conclusion and p-value will be:
A) reject the null hypothesis, and 0.01 < p-value < 0.025 
B) reject the null hypothesis, and p-value > 0.025 
C) do not reject the null hypothesis, and 0.025 < p-value < 0.05 
D) do not reject the null hypothesis, and p-value < 0.05 
E) reject the null hypothesis, p-value = 0

Quizplus · Accepted Answer

Since the test statistic is greater than the critical value at the 5% significance level (which is 9.49 for four populations and eight blocks), we reject the null hypothesis. The p-value is calculated as the probability of getting a test statistic as extreme or more extreme than the observed, assuming the null hypothesis is true. Using a chi-square distribution with degrees of freedom equal to the number of populations minus one (4-1=3), the p-value is found to be 0.0123. Therefore, the conclusion is to reject the null hypothesis, and 0.01 < p-value < 0.025.

In a Friedman Test for Comparing Four Populations, Provided That