While the internet has provided consumers with new ways to purchase goods, it also has allowed less scrupulous businesses and individuals to offer poor quality or mislabeled items. In particular, the operators of internet auction sites may not guarantee the quality or genuineness of the items...

This note develops modifications of the chi-square and maximum likelihood tests for the homogeneity of the success probabilities pi of k binomial variables when the number of trials, ni, vary widely and all pi are small. With N = [Sigma]ni, and letting the ni/N approach fixed fractions, [gamma]i...