Using the notation of the previous two exercises, let ±W1/2 be the signed square root of W, where the sign is that of Ȳ − μ0 Using the results given in

¯Section 7.4.5, or otherwise, show that Hence show that under H0

: μ = μ0

, S =

±W 1/2+(nμ0)

−1/2/6 1+(16nμ0)

−1 has the same moments as those of N(0, 1) when terms of order O(n−3/2

) are ignored. Why is it technically wrong in this case to say that S~N (0, 1) + O (n

−3/2)?