【FRM每日一题】一级：定量分析
备考FRM一级 | 2015-08-07
ABC Fund has been in existence for two years. ABC Fund has a stated objective of controlling volatility as measured by the standard deviation of monthly returns. Its average monthly return has been 6% with a standard deviation of 5%.You are asked to test the null hypothesis that the volatility of ABC Fund's monthly returns equal to 4% versus the alternative hypothesis that the volatility is different than 4%. Assuming that all monthly returns are independently and identically normally distributed, and using the tables below, which of the following choices is correct about the test to be used and what is the correct conclusion at the 2.5% level of significance?
T-table: Inverse of the One-Tailed Probability of the Student’s-Distribution
dfOne-Tailed Probability=5.0% One-Tailed Probability=2.5%
22 1.717 2.074
23 1.714 2.069
24 1.711 2.064
Chi-Square table: Inverse of the One-Tailed Probability of the Chi-Squared-Distribution
dfOne-Tailed Probability=5.0% One-Tailed Probability=2.5%
22 33.9244 36.7807
23 35.1725 38.0757
24 36.4151 39.3641
dfOne-Tailed Probability=5.0% One-Tailed Probability=2.5%
22 33.9244 36.7807
23 35.1725 38.0757
24 36.4151 39.3641
A.t-test; reject the null hypothesis
B.Chi-square test; reject the null hypothesis
C.t-test; do not reject the null hypothesis
D.Chi-square test; do not reject the null hypothesis
Answer: D
The correct test is:
Null Hypothesis:
Alternative Hypothesis:
Critical Region, reject the null if：
Therefore, you would not reject the null hypothesis. A chi-square test is a statistical hypothesis test whereby the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true.
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