- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 8. Hypothesis Tests Concerning the Mean: T-Test vs. Z-Test

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**CFA Practice Question**

Sally Duvall is estimating the mean of a population with a sample of 35 observations. The variance is unknown. Which of the following statements is FALSE?

A. Using the t-test is a more conservative approach.

B. Using the z-test is a better approach for samples greater than 30.

C. If the underlying distribution is unknown, large samples can be tested with the help of the z-test due to the central limit theorem.

**Explanation:**While the z-test is applicable for larger samples, the t-test is a more appropriate method (to be safe).

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**User Contributed Comments**
5

User |
Comment |
---|---|

danlan |
For larger samples, t-test becomes close to z-test, it's why it's acceptable to use z-test instead. |

krisc |
Can z- test be used if the population variance is unknown??? If not, then how is A) correct??? |

adam08 |
yes it can be as long as the sample is large enough (# > 30). |

kellyyang |
adamO8, I think that you can not use Z test for population variance is unknown. However, if the population variance is unknown, and sample size n>30, you can use the t-test. |

nostalgia |
if the population variance is unknown, and n >30, you can use both the z-test and the t-test, but the t-test would be the better approach. if the population variance is known, you must use the z-test. |