- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 11. Hypothesis Tests Concerning a Single Variance

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**CFA Practice Question**

Consider the following information about a fund. The fund has been in existence for 3 years. Over this period it has achieved a mean monthly return of 3% with a sample standard deviation of monthly returns of 5%. It was expected to earn a 2.5% mean monthly return over the 3-year period.

You want to test a claim that the investment disciplines of the fund result in a standard deviation of monthly returns of less than 6%.

At the 0.05 level of significance, ______

A. we are unable to make a decision.

B. we do not reject the null hypothesis.

C. we reject the alternative hypothesis.

**Explanation:**At the 0.05 level of significance, we reject the null hypothesis.

χ

^{2}= [(n - 1) s

^{2}] /σ

_{0}

^{2}= 35 x 5

^{2}/6

^{2}= 24.306

On the table at 35 degrees of freedom under the 0.95 column, we find the χ

^{2}value. We use 50 since there is no value for 35. At 50, the value is 34.764.

We will fail to reject the null if we find that chi-square is less than 34.764. 24.306 is less than 34.764, we fail to reject the null hypothesis.

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**User Contributed Comments**
10

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

Pooh |
See section C (k). |

wollogo |
If you reject the alternative hypothesis you are accepting the null hypothesis. |

nike |
Failed to reject does not mean accept. |

Xocrevilo |
Can anyone explain an easy way to know that this a chi-squared test question? |

chamad |
whenever you are testing variances (in this case std dev) use chi-square test. |

chamad |
On the table there is 30df. So Why do we have to take 50df instead. The difference in chi-sq value is huge (18.493 for 30df vs 34764 for 50df)?. Note also that have we used 30df, the result will be completely different:24.306 is greater than 18.493----Reject the NUL H!!! |

Mariecfa |
Chamad is correct about the degreea of freedom. If 30 is closer to 35 then 50 is to 35, then 30 should be chosen. Most Chi Tables have 1 t0 40 Degrees of freedom then it jumps to 50, 60, 70, 80, 90, and 100. |

Benn09 |
How do we know degrees of freedom without a sample size? Or am I missing something huge...? |

chiodom1 |
Benn09 3 years = 36 months = sample size |

weebe |
Ho : variance >= 36% (null) Ha : variance < 36% (alternate) Significance = need 0.05 in left tail (or 0.95 in right tail as table is according to right tail) Critical value (0.95, df=50) = 34.764. My question is Left tail should be rejection region (because H1 : variance < 36). And if test-statistic is lesser than critical value, then we should reject Ho. Why is the explanation of the answer opposite? It says because it's lesser that's why we will not be able to reject H0 but it seems like we should be able to. |