- CFA Exams
- CFA Exam: Level I 2021
- 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 4 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 4-year period.

B. reject alternative if χ

C. reject null if χ

D. accept null if χ

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%. The rejection point(s) for this hypothesis test at the 0.05 level of significance indicate that you would ______.

A. accept null if χ

^{2}is less than 34.764B. reject alternative if χ

^{2}is less than 34.764C. reject null if χ

^{2}is less than 34.764D. accept null if χ

^{2}is greater than 34.764Correct Answer: C

This is a chi-square test. The rejection point(s) for this hypothesis test at the 0.05 level of significance indicates rejecting null if χ

^{2}is less than 34.764.This is found across 48 degrees of freedom (4 years = 48 months) under the 0.95 column. We use 50 since there is no value for 47. At 50 the value is 34.764. We will reject the null hypothesis if we find that chi-square is less than 34.764.

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**User Contributed Comments**
10

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

tabulator |
Tricky one! |

Thajju |
What is H0 here? if H0 <= 6% then how can we reject null when chi square is less than 34.764. If H0 is assumed >= 6% then we can reject null. Can anybody shed somelight |

whiteknight |
why should we look under 0.95 column....why not under 0.05 (for significance level) ? |

thekapila |
You dont even have to calculate or determine the value 34.764. H0 <=6 That means reject null if chi sqr is less than some value.which is only 34.764 in all options. |

achu |
Thajju and whitenight have the same issue. If H0 >=6% is assumed, then it's a left tail test and the .95 column is needed because the critical region is the LEFT handed' 5% area (.95 = area to the right by definition of table). Looking at section L, it seems like we can assume H0 is >.06 because we want to "prove" Ha that sigma <.06. By putting the desired result to prove in the alternative, we strive to reject H0 null, which will mean accepting the alternative. |

tom1980 |
since accepting wasn't a right word to use in hypotheis, instead of "do not reject". therefore, A and D can be eliminated from above. If the null is stated as H0>= 0.06, then the probability value chose should be 0.95, and we reject null if λ2 is less than 34.764 |

chamad |
Tom 1980, you are right. Thanks. Just to add that the rejection point refers to rejection of the null hyp H0. So the only correponding answer is C (reject null...). This question is telling us tu use logic before going through the long way of calculation |

panvino |
No calculation needed for this one. Ho: >= 0.06 Ha: <0.06 (you want to test stdev is less than 0.06 - alternative is always expressed as what it is you want to determine). Just look at the sign of Ha to know when to reject, that is, here Ha < 0.06 therefore reject Ho if χ2 < 34.764. The opposite is also true: if Ha > value, reject null if test statistic is > than critical value. |

johntan1979 |
I never knew you need to consider direction of Ha to determine reject null when test value is > critical value. Reject null if test > critical in ALL cases for chi square test. |

sgossett86 |
I hate my life right now |