- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 6. Confidence Intervals for the Population Mean

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**CFA Practice Question**

Calculate an 80% confidence interval for a population mean. You have a sample of 21, a sample mean of -25%, and a sample standard deviation of 10%. The sample appears to be approximately normally distributed.

A. [-26%, -24%]

B. [-28%, -22%]

C. [-27%, -23%]

**Explanation:**Based on the data given, we should use the t-distribution. The critical value will be based at t_(0.10, 20) and is 1.325. Our confidence interval will then be [-25% - 1.325*(10%)/(21

^{0.5}), -25% + 1.325*(10%)/(21

^{0.5})] = [-28%, -22%].

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**User Contributed Comments**
11

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

aallali |
We use n instead of n-1 in the standard error formula, but the degrees of freedom is n - 1. |

markhuang |
because it's a t-test. |

panvino |
I think aallali is right - the standard error formula is s/(n)^1/2,even if it is a t test. For degrees of freedom we use n-1. |

zed888 |
how are we supposed to memorize the t values - especially at the 80% confidence level? |

dipu617 |
How did they get 1.325? |

AnalystBklyn |
t values will be provided on the test, zed |

Shaan23 |
I memorized all the t values. It was fun. |

GBolt93 |
Pretty sure neither t nor z values are provided on the test. However you can calculate the standard error as .021 and have to know the critical for 80% will be greater than 1 therefore b is the only logical answer. |

John_Vesce |
Pretty sure the tables are provided |

1a2a |
The tables are not provided and so questions like this one are dumb and a waste of time. I would know because I've failed this exam 2 times in a row and with my luck it'll probably be #3 coming up this December. |

gbertini |
Why are we using a t distribution rather than a z distribution in this case? |