- 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**

Consider the following statements:

II. When sample size is small and population variance is not known, the t-distribution is used.

III. The use of a t reliability factor is appropriate when the population variance is unknown but we have a large sample and can rely on the central limit theorem to ensure approximate normality of the distribution of the sample mean.

I. The t-distribution is a symmetrical probability distribution defined by a single parameter known as the degrees of freedom.

II. When sample size is small and population variance is not known, the t-distribution is used.

III. The use of a t reliability factor is appropriate when the population variance is unknown but we have a large sample and can rely on the central limit theorem to ensure approximate normality of the distribution of the sample mean.

Which is true?

A. I and II

B. I and III

C. I, II and III

**Explanation:**Some facts about the t-distribution are:

- The t-distribution is a symmetrical probability distribution defined by a single parameter known as the degrees of freedom.
- When sample size is small and population variance is not known, the t-distribution is used if the population is normally distributed (this is unknown in this question).
- The use of a t reliability factor is appropriate when the population variance is unknown but we have a large sample and can rely on the central limit theorem to ensure approximate normality of the distribution of the sample mean

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**User Contributed Comments**
5

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

armanaziz |
The two critical factors are large sample size and normality assumption. Sample size large -> Use Z or T Sample size small -> Normality assumed -> Population Variance Known -> Use Z or T Popolation Variance Unknown -> Use T Normality cannot be assumed -> Nothing will work. |

jpducros |
Has anyone managed a clever way to remember this ? |

natulik1 |
God damn it! |

Sheeb |
just because it failed to mention that it was "normally distributed". Brutal. |

thanhb91 |
The way i remember it is 1) Determine if population variance is known or unknown; if known use z, unknown follow 2 2) Determine if normally distribute or non-normal 3) If normal use t for both large and small sample size; if non-normal use t for large size only (CLT assumption) |