- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 8. Hypothesis Testing
- Subject 2. Null Hypothesis and Alternative Hypothesis

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**CFA Practice Question**

An analyst conducts a significance test to determine if the relation between two variables is real or the result of chance. His null hypothesis is that the population correlation coefficient is equal to zero and his alternative hypothesis is that the population correlation coefficient is different from zero. He gathers the following information:

Critical value at the 0.05 significance level: 1.96

Critical value at the 0.01 significance level: 2.58

Value of the test statistic: 2.8092

Critical value at the 0.05 significance level: 1.96

Critical value at the 0.01 significance level: 2.58

The analyst most likely conducted a ______.

A. one-tailed test and can reject his null hypothesis

B. two-tailed test and cannot reject his null hypothesis

C. two-tailed test and can reject his null hypothesis

**Explanation:**Because the alternative hypothesis is that the correlation is different from zero (either above or below zero), the analyst conducted a two-tailed test. Because the test statistic is greater than either of the critical values, the analyst can reject the null hypothesis.

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