- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 5. Sampling and Estimation
- Subject 5. Confidence Intervals for the Population Mean and Selection of Sample Size

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**CFA Practice Question**

To estimate the average length of their employee's telephone calls to within 0.1 minutes at a 90% confidence level, FoneJack, Inc. must randomly sample how many employee phone calls? (The population can be assumed normal with a standard deviation of 0.8 minutes.)

B. 14

C. 174

A. 169

B. 14

C. 174

Correct Answer: C

We work with the formula for E, solving it for n, the sample size. First, a 90% level of confidence; we need z(0.05). Going to the normal table, we get z(0.05) = 1.645. Now, working with the E formula, we get n = 173.1856. So, the sample size needed is n = 174 (if there is a decimal part, we always go to the next whole number).

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**User Contributed Comments**
3

User |
Comment |
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NikolaZ |
or you can use... n = (z*standard deviation)^2 = 1.73186 Simply multiply that by 100 |

sgossett86 |
yeah but what if the standard of error would have been different, say .2... what you're saying to do wouldn't have worked nikola |

robbiecow |
Someone correct me if I'm wrong, but the math seems wrong here. If you want the width to be .1, then you do the following: (xbar - 1.645*.8/sqrt(n)) - (xbar + 1.645*.8/sqrt(n)) = .1 = 2(1.645(.8/sqrt(n)) = .1 ...some basic math... n = 692.7424 |