- 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

###
**CFA Practice Question**

To estimate the average cost of a food-shopping event, Delcore Inc. randomly sampled 100 shoppers and found a sample mean of $72. Assuming a population standard deviation of $5, a 99% confidence interval for average cost for the food-shopping event is ______.

A. $70.71 < m < $73.29

B. $71.18 < m < $72.82

C. $59.12 < m < $84.88

**Explanation:**For a 99% confidence interval, we find z(0.005), the cutoff for the top 0.5% of the normal distribution. Looking up 0.995 in the middle of the table, the reading to the row/column values, we get 2.575. Working with the formula for E, we get E = 1.29. So, the 99% confidence interval is $72 - 1.29 < m < $72 + 1.29 or $70.71 < m < $73.29.

###
**User Contributed Comments**
11

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

danlan |
Where comes the value 2.575? |

danlan |
From z-table, z(2.575)=0.495, then we get 1.29=2.575*5/sqrt(100) |

dimanyc |
Why do we use 5/sqrt(100) when we the st dev of the population is known and the sample is large? |

TonyShen |
Because we are using the Sample Mean instead of the Pop Mean. |

dipu617 |
I dont see the z-table in the question. Will it be provided in the exam? |

floydbite |
not necessarily for 90, 95, 99% values |

tflies51 |
What is the formula for E? |

philerup |
Memorize 90->1.65, 95->1.96. 99->2.58 |

mmccoy |
Where does 1.29 come from? |

megageorge |
Exactly, whats formula for E? |

chris21Feb |
E = 2.58 x 5 / sqrt(100) = 2.58 / 2 = 1.29 |