- 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

###
**CFA Practice Question**

100 items are sampled from a normal distribution. The sample mean is 10 and the sample standard deviation is 2; a 95% confidence interval for the sample mean must lie between ______.

B. 9.324 and 10.676

C. 9.108 and 10.892

A. 9.608 and 10.392

B. 9.324 and 10.676

C. 9.108 and 10.892

Correct Answer: A

###
**User Contributed Comments**
7

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

aigulb |
10+-1.96*2/100^.5 1.96*2/100^.5=0.392 10-0.392=9.6 while 10+0.392=10.392 |

vinooka |
since we don't know the population standard deviation, are we not supposed to use t-tables instead? |

stevecfa |
the sample size is 100, way over 30 so the z-value is very close the t-value. |

johntan1979 |
Keyword is "normal distribution". Whenever you see that, Z is first choice. |

Shaan23 |
Kind of odd cause in the notes it says if the population variance is normally distributed and the population variance is unknown use the t test IRRESPECTIVE of the sample size. |

Shaan23 |
Add on to my comment. It doesnt state in the question if the pop variance is known or unknown...maybe thats why they use z.... |

Shaan23 |
So people read my previous two comments. The first comment is straight from the notes and is true. Use the t test. When using the t test when using the t table with n=100 it is very close to the Z score because of the large sample. So in conclusion go with the notes and know how to use each test. |