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Difference of mean profits

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Strategies A and B are tested independently, each on $n = 100$ days. The daily profit standard deviations are $6$ for A and $8$ for B. The interval for the difference of the mean profits has half-width $h = 2 \times SE$ , where $SE = \frac{6 ^{2}}{100} + \frac{8 ^{2}}{100}$ . What is $h$ ?

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Hint

Variances of independent estimates add.

Solution

Compute $\frac{6 ^{2}}{100} = 0.36$ .
Compute $\frac{8 ^{2}}{100} = 0.64$ .
The sum is $0.36 + 0.64 = 1$ , so $SE = 1$ .
Then $h = 2 \times 1 = 2$ .
So the half-width is $2$ .

Answer: $2$

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