- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 8. Hypothesis Testing
- Subject 1. The Process of Hypothesis Testing

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**CFA Practice Question**

In testing a hypothesis using a statistic Y, a critical region is chosen to meet which of the following conditions:

II. The probability of Y falling in the critical region when the alternative hypothesis is true is greater than of it not falling in the critical region.

III. The sample size is large.

I. The probability of Y falling in the critical region when the null hypothesis is true is alpha.

II. The probability of Y falling in the critical region when the alternative hypothesis is true is greater than of it not falling in the critical region.

III. The sample size is large.

A. I and II

B. II and III

C. I and III

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**User Contributed Comments**
6

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

RichWang |
What is ALPHA? |

dimanyc |
Alpha is level of significance, same as Type I error. if Alpha is 0.05%, there is a 5% prob-ty of rejecting Ho, when it is true. |

RichWang |
When alternative hypothesis is true, we need to reject the null hypothesis. The probability of Y falling in the critical region is SMALLER than it not falling in the critical region. Could someone explain why II is correct? |

achu |
Restated, II says: IF Ha is true, there's a bigger probability of landing in the Critical region than outside it. Recall that if test stat falls in the critical region, we rejct H0 and accept Ha as true. We rejected H0 when test value falls in crit range because there was 'only ALPHA %' chance of H0 being true and landing in crit region. Put another way, there's a 1-alpha chance of Ha being true and test stat landing in the critical region (since H0 and Ha are mutually exclusive and their sum = 100% of the outcomes). |

quynhnk79 |
I think: I is type I error 1st part of II (i.e: the probability of Y falling in the critical region when the alternative hypothesis is true) is the power of the test, 1-beta. And the second part of II is type II error (beta). Normally the power of the test is greater than error II. |

edrei7 |
II is basically saying that the power (1 - beta) of the test is greater than the beta of the test. |