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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?
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.