- CFA Exams
- CFA Exam: Level I 2021
- 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**

The t-test is used when ______

II. we have small samples and know the population variance.

III. we have small samples, do not know the population variance, and the population is normally distributed.

IV. we have large samples and know the population variance.

I. we have large samples and do not know the population variance.

II. we have small samples and know the population variance.

III. we have small samples, do not know the population variance, and the population is normally distributed.

IV. we have large samples and know the population variance.

Correct Answer: I and III

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**User Contributed Comments**
6

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

dnoyelles |
why not II? |

tom1980 |
if the population variance is known , then we use the z test |

chamad |
I thought we still may use t-test in II and IV but we can not use z-test in I nad III. So my answer was all of them! |

cleopatraliao |
@chamad note that the key word here is population variance.If population variance is known, use z test. |

johntan1979 |
II is assuming normal distribution, which is not stated, hence, t is more appropriate. |

Shaan23 |
First time I've seen Senor John1979 wrong. If we have a small sample regardless of if we know the variance or not AND it is not normal....there's NO test we can do. Cant do Z or T test. |