### CFA Practice Question

There are 434 practice questions for this study session.

### CFA Practice Question

Consider the following statements:

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 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)