If we assume that alpha is fixed at the 'usual' value of 0.05, this leaves only sample size available for manipulation. Deciding on an appropriate sample size depends on an ability to measure power. Unfortunately it is not always easy to estimate power. For example, suppose that you were testing a new drug that was said to reduce blood pressure. In fact this raises some philosophical points about hypothesis testing in general.
Aircraft noise has an effect on sleep.
The null hypothesis states that the presence of aircraft noise has no effect. We might be very surprised if this was true. Probably not, because the effect is too small to be of biological significance. In addition, demonstrating such a small effect would require a very large trial. Thus, although our null hypothesis is framed in terms of ' no effect' we actually mean ' no biologically significant effect'.