- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 9. Hypothesis Tests Concerning Differences between Means

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**CFA Practice Question**

MicroBulbs manufactures light bulbs that they claim have an average life of 1000 hours. To test MicroBulb's claim, a consumer group takes a random sample of 15 of the bulbs and obtains a sample mean of 950 hours with a sample standard deviation of 50 hours. For a hypothesis test at the 10% level of significance, the critical value will be ______.

A. -1.761

B. -1.645

C. -1.345

**Explanation:**Because the sample standard deviation is used (population standard deviation is unknown), a t-distribution is used. We find t(0.1, 15 - 1). Looking under column 0.10 and down to row 14, we get 1.345. The rejection region is to the left, so the critical value is -1.345.

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**User Contributed Comments**
17

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

gelonik |
Isn`t it a two tail test? |

SnowWhite |
No, the consumer group doesn't care if the light bulb lasts longer. |

art1997 |
One tail test was used : Ho m>=1000 ( > or < => one tails) |

tenny45 |
I don't understand how we're supposed to know this during the actual exam because no charts will be provided. |

mtcfa |
ALTHOUGH NOT DIRECTLY ASKED IN THE QUESTION, THE NULL AND ALTERNATIVE HYPOTHOSES ARE WRONG. SINCE THE CLAIM IS THAT THE LIGHT BULBS LAST AT LEAST 1000 HOURS, THIS IS THE ALTERNATIVE HYPOTHESES. |

rohimus |
This doesn't make sense. we are trying to determine if the bulbs last greater or less than 1000 hours. so it should be 2 tailed. |

hizmo |
Snowhite is correct. on mtcfa's remark. If you use Ho: u <= 1000 you will still get the same results. ie you will now accept Ho since your critical area is on the right side while your test value is way left. |

labsbamb |
fellows, can someone can provide the t critiacl value for a T test at 90%,95% and 99% confidence intervalle? |

Janey |
From the question you can tell that it is one-tailed as all the possible answers are only one sided and the question only asks for one. |

Bevin |
labsbamb, it depends on the degrees of freedom (n-1). We can't memorize the answers for the t-distribution. |

aprilapple |
How is the test value of -3.87 derived? |

mazo86 |
Why the Ho is U>0 1000... it should not be U = 1000?? |

mazo86 |
I just got it... Now it's clear to me |

bloomt |
can someone help with aprilapple's question? I don't see what they mean by 'test value' here |

endurance |
The test value is derived as: t = Xbar-mean divided by sample deviation/square root n -> (950-1000)/(50/sq.root 15)= -3,87 |

Rachelle3 |
Thanks endurance! |

odum612 |
In my view a 2 tail test should be applied, given that the null hypothesis should be structured based on the population distribution. The question states that " MicroBulbs manufactures light bulbs that have an average life of 1000 hours..." therefore the null hypothesis is (Population Mean = 1000 hours) . this makes the question a two tail test. |