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**CFA Practice Question**

An analyst is testing for the variance of an index. His conjecture is that the index variance is 196. From a sample of 19 observations, he estimates the historical standard deviation to be 16. Based on the null hypothesis of equality can he accept the null at 5% alpha? What is the calculated statistic?

A. No, 15.75.

B. Yes, 23.51.

C. Yes, 13.78.

**Explanation:**The test to be used is Chi-squared, χ

^{2}. It is applied as χ

^{2}= (n - 1)s

^{2}/σ

^{2}= (18 x 256)/196 = 23.51. Since this is less than the critical value of 28.87 at 18 degrees of freedom, we cannot reject the null hypothesis.

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**User Contributed Comments**
4

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

antony |
Are we provided w/ these tables on the exam? How are we to know that the critical value is 28.87 at 18 degrees of freedom? |

gweiden |
For this question, you don't need the tables. The only answer that makes sense is B because the calculated statistic is 23.51. None of the other answers give you 23.51 as the calculated statistic. |

nick1981 |
chi square, as an equality test, is two tailed and the explanation should point out that you have to look at the interval before rejecting, not only at the upper side. any comments on this?? |

Gleeder |
antony - The CFA website says they will not provide tables and notes that we will not need tables because all info will be provided in the questions. |