Item-by-item sampling for promotional purposes

In this paper we present a method for sampling items that are checked on a pass/fail basis, with a view to a claim being made about the success/failure rate for the purposes of promoting a company’s product/service. Attention is paid to the appropriate use of statistical phrases for the claims and this leads to the development of Bayesian credible intervals. The hypergeometric distribution is used to calculate successive stopping rules so that the costs of sampling can be minimised. Extensions to the sampling procedure are considered so as to allow the potential for stronger and weaker claims to be made as sampling progresses. The relationship between the true error rate and the probabilities of making correct claims is discussed.