like if the variance of your result is really high and you're estimating the mean its clear that the number of samples you take is important !?!
To complicate matters further, "accuracy" is an extremely tricky concept in statistical analysis because error rates work very differently than they do in, say, physics. In physics, when you measure something you can be sure that your results are accurate, so long as you stay outside your instrument's range of error. In stats, your confidence interval just tells you how likely it is that your results are completely wrong, or even worse, wrong by a completely unknown amount. Every statistical inference you make has a chance of completely blowing up on you. That chance can be defined and reduced, but it can never be eliminated. There's also things like frequentist vs Bayesian statistics, where the interpretation of the same data can be completely different.
Zed may be a jerk sometimes, but on this topic he's dead right. Most programmers are far more confident about this stuff than they should be.