Number of samples to use in estimating sinewave amplitude in the presence of noise

The number of samples required to estimate the amplitude of a digitized sinewave depends on the amount of additive noise present, more specifically, on the precision of the estimator used which is depends directly on the additive noise standard deviation. Here an analytical approximate expression for this precision is derived and then used to derive an analytical expression useful in computing the minimum of number of samples that should be acquired to guarantee a given bound on the prevision of the sinewave amplitude estimates.