ST: ASM 2nd edition, 2nd printing. Exercise 10.16

This question seems simple enough, however, the answer misses that the denominator is actually the sum of 4 squares rather than 3. This problem perplexes me because while the random variables are standard normal, the denominator is the unbiased sample variance or X1,...,X4. S^2 would be the sum of 4 squares divided by 3 with d.f.=3. To me, this implies that the numerical answer based on F(2,3) is correct but the narrative has the simple error stated above.



However, my mind just won't let it go without confirmation.

ST: ASM 2nd edition, 2nd printing. Exercise 10.16