题目
A fund of funds has investments in 36 hedge funds. At the end of the year, the meanreturn of the constituent hedge funds was 13.0%. The standard deviation of the funds' returns was 9.0%. The benchmark return for the fund of funds was 10.0%. With 95.0% confidence, can we accept the one-sided alternative hypothesis that the fund of funds exceeded its benchmark; i.e., can we reject the one-sided null hypothesis that the fund of funds' true performance is less than or equal to 10.0%?
选项
A.Yes, true fund performance is greater than 10.0% as computed t-stat of 2.00 exceeds lookup value of 1.690
B.Yes, true fund performance is greater than 10.0% as computed t-stat of 2.00 does not exceed lookup value of 2.030
C.No, true fund performance is not greater than 10.0% as computed t-stat of 2.00 exceeds lookup value of 1.690
D.No, true fund performance is not greater than 10.0% as computed t-stat of 2.00 does not exceed lookup value of 2.030
答案
A
解析
True fund performance is greater than 10.0% as computed t-stat of 2.00 exceeds lookup value of 1.690.Standard error = 9.0%/√36 = 1.5% and the computed t-stat = (13.0% - 10.0%)/1.5% =2.00.The one-sided lookup value with 35 degrees of freedom = T.INV(95%,35) = 1.690.Because 2.00 > 1.690, we can reject the one-sided null. Note if the null hypothesis were two-sided, the lookup value would be 2.030 and we would not reject at 95.0%.当计算出的2.00的t-stat超过查找值1.690时，真实基金的绩效大于10.0％。标准误差= 9.0%/√36 = 1.5%以及计算出的t-stat =（13.0％-10.0％）/ 1.5％= 2.00。具有35个自由度的单侧查找值= T.INV（95％，35）= 1.690。由于2.00> 1.690，我们可以拒绝单侧null。 请注意，如果原假设是双向的，查找值将为2.030，而我们不会拒绝95.0％。