- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 12. Hypothesis Tests Concerning Differences between Variances

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**CFA Practice Question**

You are investigating whether the population variance of returns on the S&P 500 changed subsequent to September 11, 2001. You gather data for 20 months before and after September 11.

Before September 11: 20 | 2.987 | 6.987 | 48.818

After September 11: 20 | 2.435 | 4.987 | 24.870

n | Mean Monthly Return | Standard Deviation | Variance

Before September 11: 20 | 2.987 | 6.987 | 48.818

After September 11: 20 | 2.435 | 4.987 | 24.870

At the 0.01 level of significance, ______

A. we reject the null hypothesis.

B. the critical value is 1.962.

C. we fail to reject the null hypothesis.

**Explanation:**At the 0.01 level of significance, F = 48.818/24.870 = 1.963.

We use F tables at the 0.005 level (0.01/2) and we have a value of 3.4. 1.963 is less than the critical value of 3.4, so we fail to reject the null hypothesis.

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**User Contributed Comments**
7

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

Pooh |
F-test: equality of variance of two normal populations. |

hellboy18 |
Sorry, Can someone tell me how we find the F-Table value of 3.4? I am looking at these F-Tables: downloads.hawkeslearning.com/Docs/StatisticsTables/F-Table%20with%20alpha%20at%200.005.pdf |

homersimpson |
Hellboy18: make sure you are reading the 0.005 F-dist Table. Search the intersection "15-20" and "19". You will find 3.4 |

maria15 |
I like how all the names on the comments in here are all movie/tv characters lol |

maria15 |
Can someone please explain how to get 3.4 from the F-table? Homersimpon's suggestion is not working for me. Thanks! |

ColonelCFA |
I have found that by memorizing the lowest number on the "common" F-Table (2.62) I have been able to answer almost all of the F-Test questions. |

birdperson |
df(19,19) significance level (0.005) = 3.4317 |