- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 5. Sampling and Estimation
- Subject 5. Confidence Intervals for the Population Mean and Selection of Sample Size

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**CFA Practice Question**

Calculate a 90% 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. [-28.9%, -21.1%]

B. [-27.9%, -22.1%]

C. [-28.1%, -21.9%]

**Explanation:**Based on the data given, we should use the t-distribution. The critical value will be based at t_(0.05, 20) and is 1.725. Our confidence interval will then be [-25% - 1.725*(10%)/(21

^{0.5}), -25% + 1.725*(10%)/(21

^{0.5})] = [-28.9%, -21.1%].

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**User Contributed Comments**
15

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

danlan |
Since we use sample standard deviation, we suppose the population variance is unknown, so we use t-distribution. |

samsonov |
should they have 20 or 21 in devisor? |

Criticull |
can we get critical values with the BAII Plus? If not I assume they provide tables. |

markhuang |
21. 20 is the degree of freedom when getting the critical value, but 21 is used to calculate standard error. |

mpapwa22 |
Thanks Markhung, this is very clear now, was getting really confused with the 20 or 21. |

sargutin |
I am using the equation in the explanation and get a [-28.76 ,-21.236] interval. Am I doing something wrong, or the multiple choice is just really not precise? |

jpducros |
I got the same as you Sargutin. I seems they used 20 instead of 21 in their formula to reach their result. |

maria15 |
Can someone please explain how to get 1.725 from the t-distribution? I completely forgot. Thanks! |

maria15 |
Never mind. I checked my book and got it. Thanks! |

Shaan23 |
N - 1 DF guys. |

chris297 |
So the fact that it is approximately normally distributed would not lead to the usage of normal distribution table? |

SalimBouch |
no because you should estimate the standard deviation of the population using the standard deviation of the sample |

thanhb91 |
I heard they wont give you the table, so we should be remember some critical number!! |

dbalakos |
Such questions with critical values of t-distribution wont be in the exam since we wont be provided with tables. Just memorize important levels of significance from z-table and you will be fine. |

Patdotcom |
Are we sure that t is 1,725? I used it first and the figures were as sargutin said(-28,8;21,2). I tried then with t(0,1,20) t=1,325 and then option b was exactly... |