A chi-square test of a contingency table with 4 rows and 5 columns shows that the value of the test statistic is 22.18. The most accurate statement that can be made about the p-value for this test is that:
A) p-value is greater than 0.05
B) p-value is smaller than 0.025
C) p-value is greater than 0.025 but smaller than 0.05
D) p-value is greater than 0.10
E) Not enough information is given to determine the p- value.

Question

Quizplus · Accepted Answer

Since we have 4 rows and 5 columns, the degrees of freedom for this test would be (4-1) x (5-1) = 12.
Using a chi-square distribution table or calculator with 12 degrees of freedom, we can find that the critical value for a 0.05 level of significance is 21.03 and the critical value for a 0.025 level of significance is 24.72.
Since the calculated chi-square value of 22.18 falls between these two critical values, we can conclude that the p-value for this test is greater than 0.025 but smaller than 0.05. Therefore, the most accurate statement about the p-value is C: "p-value is greater than 0.025 but smaller than 0.05."

A Chi-Square Test of a Contingency Table with 4 Rows