(3.48) and XXXXXXXXXXcan be verified with the aid of the Hoeffding inequality and (3.49). Let Tn = 1 2 (n + S 0 n ) with S 0 n defined in XXXXXXXXXXThen Tn ∼ Bin(n, 1/2) under H0, and hence, S 0 n is...

(3.48) and (3.50) can be verified with the aid of the Hoeffding inequality and (3.49).

Let Tn = 1 2 (n + S 0 n ) with S 0 n defined in (3.72). Then Tn ∼ Bin(n, 1/2) under H0, and hence, S 0 n is distribution-free under H0 and n −1/2S 0 n D→ N (0, 1) as n increases.