Z-test or t-test

CFA Level I
#1

I am a bit confused with this question: an analyst wants to test a hypothesis concerning the population mean of monthly returns for a composite that has exists for 24 months. The analyst may appropriately use:
a. a t-test not a z-test if returns for the composite are normally distributed. This is the correct answer in the book.

However, I chose (b). “either z-test or t-test if returns for the composite are normally distributed” because I think when the composite are normally distributed, z-test can be used (regardless of the sample size) given that the population variance is known. If the variance is unknown then t-test will be used. Here the question does not mention anything about variance, so I assume that either of them can be used depending upon the availability of the population variance (answer B). However, the right answer is A for which z-test is not used. Can someone enlighten me on this please. I appreciate it.

#2

If they don’t tell you that the population variance is known, you can’t assume that it is.

1 Like
#3

oh yeah, it makes sense :smile: Thank you.

#4

My pleasure.

#5

So its fine to assume variance is unknown, Right?

#6

They’ll tell you whether it’s known or unknown.

#7

Ok👍