# Chi Square

Hi,

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?

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I agree with you.

Where did you get this question?

Simplify the complicated side; don't complify the simplicated side.

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my statistics book seem to agree with the answer.

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

in this case,

H0 : sigma = .06

H1 : sigma < .06 (original claim)

Ah … you didn’t say that 10.1 was the lower critical value.  I was thinking that it was the upper critical value.

I admit that I haven’t looked at a chi-square table in a while, so I don’t have a good feel for the magnitude of the critical values.

Simplify the complicated side; don't complify the simplicated side.

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there are three kinds of Xtests.

1) if you are testing the claim volatility < some number K, use the left-tailed test

2) if you are testing the claim volatility > some number K, use the right-tailed test

3) if you are testing the claim that volatility is not equal to some number K, use the two-tailed test

for this problem, you are testing if the volatility is less than some number, so you need to do a left-tailed test

wow. perfect!!! thanks so much, everyone for clarification:)

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Test_20 wrote:

Hi,

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?

It’s a left-tailed test (i.e. less than 6%) so the 5% rejection point is on the left hand side of the distribution. Your rejection decision should be:

- Reject H0 if chi-sq test statistic < 10.1

- Do not reject H0 if test statistic > 10.1

Since the test statistic is 13.19, so hence you cannot reject H0.

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