- 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 length of their employees' telephone calls, FoneJack, Inc. randomly sampled 25 employee phone calls. If the sample mean was 1.3 minutes and the population can be assumed normal with a standard deviation of 0.3 minutes, a 90% confidence interval for the phone calls is ______.

A. 1.2 < m < 1.4

B. 1.24 < m < 1.36

C. 1.18 < m < 1.42

**Explanation:**For a 90% confidence interval, we find z(0.05), the cutoff for the top 5% of the normal distribution. Looking up 0.95 in the middle of the table, the reading to the row/column values, we get 1.645. Working with the formula for E (see top right), we get E = 0.1. So, the 90% confidence interval is 1.3 - 0.1 < m < 1.3 + 0.1 or 1.2 < m < 1.4.

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**User Contributed Comments**
4

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

dimos |
1.3-{1.65*(0.3/5)}< m < 1.3+ {1.65*(0.3/5)} = 1.2 < m < 1.4 |

Marinov |
Aren't we supposed to use the t-distribution here? We neither know the population mean, nor the sample is large. |

charliedba |
@Marinov: you are given the population standard deviation already. use z-test. |

sevywonder |
We also don't get tables on the test. |