Statement-1: In a small segment of string carry the sinusoidal wave, total energy is conserved.
Statement-2: Every small part moves in S.H.M. and total energy of S.H.M. is conserved.

The Transmitted power at any point on the string (executing wave motion) is given by: $P=\frac{{\omega }^2{A}^{2}F{\cos }^2(\omega t-kx)}{v}$

The Total energy (up to time ‘t’) $={\int }_0^{t}Pdt$

The total energy varies with time (for each point), only the average Power delivered is independent of time. Hence the assertion is False. However energy for the entire string would be conserved. From the wave equation