CFA Practice Question

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CFA Practice Question

You are thinking of using a t procedure to construct a 95% confidence interval for the mean of a population. You suspect that the distribution of the population is not normal and may be skewed. Which of the following statements is correct?

A. You should not use the t procedure because the population does not have a normal distribution.
B. You may use the t procedure, provided your sample size is large, say, at least 30.
C. You may use the t- procedure because it is robust to non-normality.
Correct Answer: B

t procedures are robust against non-normality of the population except in the case of outliers or strong skewness. Guidelines are:
  • sample size less than 15: use a t procedure if the data are close to normal. If the data are clearly not normal or if outliers are present, do not use a t procedure.
  • sample size at least 15: a t procedure can be used except in the presence of outliers or strong skewness.
  • large samples: t procedures can be used even for clearly skewed distributions when the sample is large, roughly n >= 30.

User Contributed Comments 6

User Comment
pisanc06 Does this contradict the previous question?
NikolaZ No it does not, since when the sample size exceeds 30, it is best to use the z-table as it is more precise.
johntan1979 There is no mentioning whether pop var is known or not. So t is preferable.
sgossett86 I made a six column four row chart with headings in the first two rows, kinda like a matrix, to visualize conditions where the respective tests are applicable.
cumc can someone please give me more details ?
gc1210 @johntan1979, as long as the sample size is large we could use either t or z (regardless of knowing the population variance or not), why is there a preference towards t? Is it just because t gives a more conservative answer?
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