  The aim of the present paper is to estimate and control the Type I and Type
II errors of a simple hypothesis testing problem of the drift/viscosity
coefficient for stochastic fractional heat equation driven by additive noise.
Assuming that one path of the first $N$ Fourier modes of the solution is
observed continuously over a finite time interval $[0,T]$, we propose a new
class of rejection regions and provide computable thresholds for $T$, and $N$,
that guarantee that the statistical errors are smaller than a given upper
bound. The considered tests are of likelihood ratio type. The main ideas, and
the proofs, are based on sharp large deviation bounds. Finally, we illustrate
the theoretical results by numerical simulations.
