- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 6. Confidence Intervals for the Population Mean

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**CFA Practice Question**

To estimate the average weight of the red-crowned woodpecker to within 2 grams at a 95% confidence level, researchers must randomly sample how many red-crowned woodpeckers? (The population can be assumed normal with a standard deviation of 13 grams.)

A. 282

B. 70

C. 163

**Explanation:**We work with the formula for E, solving it for n, the sample size. First, for a 95% level of confidence, we need z(0.025). Going to the normal table, we get z(0.025) = 1.96. Now, working with the E formula, we get n = 162.3076. So, the sample size needed is n = 163 (if there is a decimal part, we always go to the next whole number).

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**User Contributed Comments**
7

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

haarlemmer |
IN FACT, IT IS WRONG. WITHIN 2 PERCENT MEANS E=1 NOT 2. |

tony1973 |
haarlemmer: within 2 grams at a 95% level, not 2%. |

danlan |
It means: 2 gram is the critical point for 95% confidence level (related to 1.96 as reliability factor) |

Janey |
I found this easier with trial and error using the equation - 1.96(.3/SQRTn) where n is either A,B,C or D |

niko7 |
haarlemmer, apparently "within 2 grams" assumes on both sides. |

Vadik |
within. I really thought in the range of 2 grams. E=1 |

birdperson |
second that vadik |