NO.PZ2023091601000063
问题如下：
A senior manager on the proprietary trading
desk of an investment bank is evaluating the performance of two fixed-income
traders, trader A and trader B, using their annual performance over the last 10
years. Trader A generated an average return of 7% with a standard deviation of
15%, while trader B generated an average return of 12% with a standard
deviation of 20%. The manager tests the null hypothesis that the traders
performed equally well against the alternative hypothesis that the average
return of trader B is higher than the average return of trader A. Assuming the
performances of each trader are independent, which of the following correctly identifies
the test statistic and the 5% critical value corresponding to this alternative
hypothesis?
选项：
A.
The test statistic
is -0.63 and the critical value is 2.31.
B.
The test statistic
is -0.27 and the critical value is 2.31.
C.
The test statistic
is 0.27 and the critical value is 1.86.
D.
The test statistic
is 0.63 and the critical value is 1.86.
解释：
D is correct. If
we let X and Y denote traders B and A respectively (noting that it is safest to
work with proportions rather than percentages) the test statistic for testing
that the means are equal (i.e., 𝐻0:𝜇𝑋=𝜇𝑌) is:
Note
that the denominator no longer has the (2σXY/n) component in the calculation;
this is because the two performance results are independent – as such, the
correlation between X and Y is 0. The statistic 0.63 follows a t-distribution
with 8 degrees of freedom and a 5% (one-sided) size of test uses the critical
value of 1.86.
老师好，为什么自由度是8而不是9，n不是10吗？
为什么结果要用绝对值？
