Suppose I wish to obtain the period of an oscillation, $T$, so I measure the time for $n$ oscillations to obtain $nT$. Suppose I use a stopwatch, so the quantity $nT$ has an uncertainty of around 0.1 seconds. How do I estimate the uncertainty in $T$?
Using the standard equation for propagating the error in $z = ax\pm b$, I'd get $\Delta T = (1/n)(\Delta (nT))$. However, I believe this is only valid when the measurements are independent, which here they're clearly not. This also implies the uncertainty would fall to zero if I took enough measurements: this doesn't seem intuitive, since there will always be some sampling uncertainty.
Is the best way to approach this to learn about a Bayesian approach, or can I still do something sensible with the traditional statistical techniques that I am familiar with?