In a one-tailed test of X2 how do you compare the critical value with the test statistical?
Example: Fund Alpha has been in existence for 20 months, during this period the standard deviation of monthly returns has been 5%. You want to test a claim by the fund manager that the standard deviation of monthly return is less than 6%? The critical value or rejection point given is a 0.05 level of significance.
Answer: X2 = 13.19 and Rejection point based on df and significance = 0.05 is 10.1 and answers says, "since the test statistic is higher than the rejection point we can NOT reject H0.
But I am confused as per my understanding since the critical point is less than the X2, H0 should be rejected! Could anyone please help me to understand?
according to my textbook, for a left-tailed chi-square test, if the test statistic is greater than the critical value (found on the table), you cannot reject the null hypothesis. that is:
critical value < test statistic: fail to reject null hypothesis
critical value > test statistic: reject the null hypothesis