- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 5. Sampling and Estimation
- Subject 5. Confidence Intervals for the Population Mean and Selection of Sample Size

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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?

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.

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.

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**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? |