- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 9. Hypothesis Tests Concerning Differences between Means

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**CFA Practice Question**

The realized mean monthly return on the S&P 500 in the 1990s appears to have been substantially different than the mean return in 2000s. The data indicate that assuming equal population variances is not unreasonable.

μ

_{1}= 1990s population mean return and μ_{2}= 2000s population mean return.The decision made in this hypothesis is (assume at the 10% level) ______.

A. to reject the null hypothesis

B. that the t-value is significant at the 0.1 level

C. not to reject the null hypothesis

**Explanation:**Pooled estimate of variance needs to be computed as follows:

S

^{2}

_{p}= [(60 - 1)(5.876)

^{2}+ (60 - 1)(4.986)

^{2}] / (60 + 60 - 2) = 29.694

Now determine the value of t. t = [(0.7 - 1.8) - 0] / [29.964/60 + 29.964/60]

^{1/2}= -1.101

We reject null if t > 1.658 or t < -1.658 (t-value: t(118, 0.05) = 1.658). The t-value of -1.101 does not fit the rejection criteria. In other words we do not reject the null hypothesis and the t-value is not significant at the 0.1 level.

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**User Contributed Comments**
3

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

chamad |
Test of equality of means |

ledyba |
why is he using the pooled variance formula if we cannot suppose that varainces are equal? |

ledyba |
nevermind, i missread the question. |