5. Let ZI"'" Z; be identically independently distributed according to a continuous distribution D, of which it is assumed only that it is symmetric about some (unknown) point. For testing the hypothesis H : D(O) = t,the sign test maximizes the minimum power against the alternatives K: D(O) s q (q < t). [A pair of least favorable distributions assign probability 1 respectively to the distributions F E H, G E K with densities 1 - 2q q )IIXIJ I{x) = 2{1 - q) ( 1 - q , g{x) = (I _ 2q)( _q )Il XlI 1 - q where for all x (positive, negative, or zero) [x] denotes the largest integer x.]