 Solution

Bootstrapping estimates sampling uncertainty by repeating an analysis on resampled data. In the ordinary nonparametric bootstrap, draw observations with replacement from the empirical sample, retaining its size, and recalculate the statistic many times. The resulting distribution can estimate a standard error, assess bias or form a justified bootstrap confidence interval. It is useful when an analytic sampling distribution is difficult to obtain.

The resampling unit must match the design: keep paired measurements together, and resample independent clusters when observations are clustered. Resampling individual ratings as if they were independent lecturers would misrepresent uncertainty. The ordinary bootstrap assumes the sample and chosen resampling scheme adequately represent the relevant data-generating variation; it does not repair selection bias, guarantee accurate inference from a tiny sample, or succeed for every statistic. Specify the interval method and computational settings, since a simple percentile interval is not universally appropriate.