- 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
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
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) |