题目
An analyst is given the task of determining whether a group of 16 active portfolio managers have achieved a significantly higher performance (using a significance level of 0.05) than the average for all portfolio managers over a certain period. Over the period of the study, the active portfolio managers achieved a mean return of 15%. Over the same period the mean return for all portfolio managers was 12% and their standard deviation was 8%. The correct conclusion from this study is that:
选项
A.The performance of active portfolio managers is significantly higher than the average for all portfolio managers.
B.The performance of active portfolio managers is not significantly higher than the average for all portfolio managers.
C.The performance of active portfolio managers is significantly lower than the average for all portfolio managers.
D.The performance of active portfolio managers is the same as the average for all portfolio managers.
答案
B
解析
The null hypothesis in this study is that the performance of active portfolio managers ≤ average for all portfolio managers. The value of test statistic for this, z = (15% - 12%)/(8%/4)=1.5. Using normal distribution as an approximation, the critical value is 1.65 (the rejection region is above 1.65). As the test statistic is lower than the critical value the null hypothesis cannot be rejected, i.e. the performance of active portfolio managers is not significantly higher than the average for all portfolio managers.本研究的零假设是，活跃的投资组合经理的绩效≤所有投资组合经理的平均值。 为此的测试统计值，z =（15％-12％）/（8％/ 4）= 1.5。 使用正态分布作为近似值，临界值为1.65（拒绝区域大于1.65）。 由于检验统计量低于临界值，因此不能拒绝零假设，即，活跃的投资组合经理的绩效不会显着高于所有投资组合经理的平均值。