On testing the correlation coefficient of a bivariate normal distribution

Summary

Here we propose two tests for testing ρ in the bivariate normal population assuming that the ratio of the variances in it is known. The first test (U.M.P.U.) is derived by using the Neyman-Pearson lemma, whereas the second test is obtained through testing the scale parameter of the Cauchy distribution. The powers of the first and second tests are compared with a well-known test, based on the sample correlation coefficient for small and large samples respectively.