Sample size determination with a pilot study

We analyse standard confidence intervals for the mean of a finite population, with a view to sample size determination. We first consider a standard method for sample size determination based on the assumption of knowledge of the population variance parameter. We then consider the more realistic case where the population variance is treated as an unknown, and we derive a new method of sample size determination that accounts for the uncertainty in this parameter. We develop a sample size calculation method based on a preliminary sample of data which allows us to increase the accuracy of our inference by some specified amount with a specified level of confidence. We compare this method to the standard method.