- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 3. The Central Limit Theorem

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**CFA Practice Question**

Which one of the following statements is correct?

A. If, for a sample of 100 students from the registrar's office, it was found that 95% of students had dean's list averages, random sampling from the entire student body could not possibly have been performed.

B. Assuming the population variance is known, if the sample size is doubled, the variance of the distribution of the sample mean of a variable would be halved.

C. If L and U are the lower and upper limits of a 99% confidence interval for μ, then μ varies between L and U with a probability of 0.99.

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**User Contributed Comments**
9

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

haarlemmer |
I guess it is not to be halved, but quartered. This is a square relationship with the sample size. Someone gives me a hand to answer it, please! |

johnsk |
sample variance = s^2/N. N is doubled so the variance is halved. |

danlan |
Mu should not vary, it is constant. |

dimanyc |
johnsk is absolutely correct |

ElenaStep |
Can you please explain why C is wrong?Thanks! |

Profache |
C is wrong because in a 99% confidence interval there are 99% chances that the mean is a value in that interval. It is incorrect to say that the mean will vary among values in a interval. |

jpducros |
Sorry I still don't get it. sample variance = s^2/N ?? |

Shaan23 |
JPDuscros. If sample variance = S^2 /n at the beginning(Eg. say n=10 ----> S^2 / 10 Now you double n ---> 20 .... Then variance = S^2 / 20 So when you double n your variance is halved |

Hungerford |
C is incorrect because a 99% CI just means that, you are 99% confident that the true value lies within that interval. The value doesn't actually have to VARY within the interval. |