- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 1. Introduction

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**CFA Practice Question**

A simple random sample of 50 undergraduates at Johns Hopkins University found that 60% of those sampled felt that drinking was a problem among college students. A simple random sample of 50 undergraduates at Ohio State University found that 70% felt that drinking was a problem among undergraduates. The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State is approximately 40,000. We conclude that ______

B. the sample from Johns Hopkins has much more sampling variability than that from Ohio State.

C. the sample from Johns Hopkins has almost the same sampling variability as that from Ohio State.

A. the sample from Johns Hopkins has much less sampling variability than that from Ohio State.

B. the sample from Johns Hopkins has much more sampling variability than that from Ohio State.

C. the sample from Johns Hopkins has almost the same sampling variability as that from Ohio State.

Correct Answer: C

The sampling variability of a statistic is primarily determined by the sample size. Larger samples have less variability. In this case, both examples have the same sample size.

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**User Contributed Comments**
7

User |
Comment |
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sivenkova |
Doesn't the proportion of the population and the sample influence the sample variability? |

dnoyelles |
i think that would affect the representativeness of the sample alone. |

bundy |
Trick Question Sample size is equal therefore the sampling variability is the same. |

geofin |
Here is what my stats textbook says about that: "As the variability of the population you're sampling from increases, the confidence interval of your sample gets wider." However, later it says: "If the population is at least 100 times a big as the sample, the variability in the statistic does not depend on the population size." The last statement is true for Ohio State but not for Hopkins (2000/50=40<100) So, technically, the correct answer should be D. None of the above: "the sample from Johns Hopkins has somewhat more sampling variability than that from Ohio State" |

johntan1979 |
No, geofin. It's a fair game. You can't say bigger populations, bigger sampling variability. Both sample sizes are the same. Common sense might tell you that choosing 50 from 40,000 will create larger sampling variability but the same can be said for 50 from 2,000. The ultimate fact remains. Sample size determines sampling variability and the larger the n, the lesser the sampling variability. |

EEEEvia |
come on guys, it's SIMPLE RANDOM SAMPLE. so C is right. |

CFAJ |
this guy arguing with a direct quotation from a statistics book |