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**CFA Practice Question**

Suppose mutual funds with standard deviations of returns less than 2% a month are classified as 'low risk'. An analyst wants to determine if a mutual fund EAR can be classified as 'low risk'. We have the following values for chi-square distribution.

chi-sq(0.025, 35) = 53.2

chi-sq(0.05, 35) = 49.8

chi-sq(0.025, 35) = 53.2

The analyst has 36 months of data in a sample of EAR returns, and finds the sample standard deviation to be 2.94%. Suppose the Null Hypothesis is that EAR is a 'low risk' stock. The analyst wants to test the Null at the 5% level of significance. What is the chi-square test statistic value, the threshold level for rejection of the Null, and the decision?

A. 50.75, 53.2 and fail to reject respectively

B. 50.75, 49.8 and reject respectively

C. 75.63, 49.8 and reject respectively

**Explanation:**The Null Hypothesis is that EAR is a 'low risk' stock, that is its variance is less than or equal to 2%. So it will be a one-tailed test with the region for rejection lying in the right tail. As the test statistic exceeds the threshold, we reject the Null hypothesis.

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**User Contributed Comments**
3

User |
Comment |
---|---|

aashishb |
how to get 75.63??? |

andrewmorgan |
(n-1)s^2/sigma^2 = (35*8.6436)/4 = 75.6315. Anyone? |

cwest020 |
(35*(.0294^2))/(.02^2) = 75.63 |