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**Basic Question 1 of 1**

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 34.764###
**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 |

I just wanted to share the good news that I passed CFA Level I!!! Thank you for your help - I think the online question bank helped cut the clutter and made a positive difference.

#### Edward Liu

**Learning Outcome Statements**

construct hypothesis tests and determine their statistical significance, the associated Type I and Type II errors, and power of the test given a significance level

*CFA® 2024 Level I Curriculum, Volume 1, Module 8.*