- CFA Exams
- 2021 CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 8. Hypothesis Tests Concerning the Mean: T-Test vs. Z-Test

###
**CFA Practice Question**

An analyst compiled the following information relating to EPS forecasts. The analyst wants to forecast quality. The test used to forecast quality is the zero-mean test, which states that optimal forecasts should have a mean forecasting error of 0.

Mean forecast error: 0.07

Standard deviation of forecast error: 0.2

B. we have committed a Type I error.

C. we accept the null.

Number of forecasts: 100

Mean forecast error: 0.07

Standard deviation of forecast error: 0.2

Using a z-test, at the 0.05 level of significance ______

A. we reject the null.

B. we have committed a Type I error.

C. we accept the null.

Correct Answer: A

Z = (0.07 - 0)/(0.2/100

^{1/2}) = 3.5.Note that the calculation of the z-statistic with unknown variance is the same as the calculation of the t-statistic. When the significance level is 0.05 the rejection points are Z > 1.96 and Z < -1.96. The computed value of Z of 3.5 is greater than 1.96; this means we reject the null at the 0.05 level.

###
**User Contributed Comments**
9

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

tenny45 |
Didn't question #4 just mention that at the 0.05 significance level, the critical value is 1.645 (instead of 1.96)? |

nick |
q4 is 10% confidence interval, but 5% for the bottom part. |

awellman |
1.645 is the one-tailed critical value. 1.96 is the two-tailed critical value. |

sapphire |
Does anybody know how to get 1.96 besides memorising it? Thanks a lot |

StanleyMo |
is that the = and < > can affect the 5% or 10% level of significance? |

thekid |
Sapphire... we know: alpha=5% and its a one sided test. Therefore, looking at the z tables we look for the value 5% (0.05)... and we find that z -1.64 has a value of 5.05% (0.0505) and z -1.65 has a value of 4.95% (0.0495). Therefore, a z of 1.645 would give us a value of 5%. If this was a two sided test with the same alpha=5%, Then you would look at the z table for a zscore with a value of 0.025 (5%/2) and if you look at the the z -1.96 it has a value of 0.025 (the value we are looking for). (Since its the same on the other tail z +1.96 = z -1.96) Summary: Given alpha=5%, with a 1sided test: 5% on EACH SIDE therefore 90% = Zscore of 1.645, with a 2sided test: (2.5%) 5%/2 on each side therefore 95% = Zscore of 1.96 |

johntan1979 |
sapphire, you can write it on a piece of paper and bring it into the exam. |

gill15 |
thekid --- this is a TWO SIDED test.....thats why the answer has 1.96 in it.. optimal forecating is u = 0 Ha u does NOT equal 0 ---- two sided test |

sumeetb |
Yes, gill15, Its a 2-tail test. My doubt is: then, do we take significance level as 10% or keep it 5? Pls help |