- 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**

If a random sample of size n = 100 from a population with s = 8 yields a sample mean of 56, then a 90% confidence interval for μ is ______.

B. 54.98 < μ < 57.02

C. 54.68 < μ < 57.32

A. -1.32 < μ < 1.32

B. 54.98 < μ < 57.02

C. 54.68 < μ < 57.32

Correct Answer: C

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, we get E = 1.32. So, the 90% confidence interval is 56 - 1.32 < m < 56 + 1.32 or 54.68 < μ < 57.32.

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**User Contributed Comments**
4

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

got2pass |
what is the formula for E? |

Poorvi |
E = z x s/(n)^1/2 |

poomie83 |
What is the deal for the top 5% cut off. Where does that come from? |

leftcoast |
The top 5% of the distribution is cut off if you want a 90% confidence interval. It's just talking about how to find the appropriate z-score. Easier to just memorize the 90% z-score. |