Rearranging the Labels

Group A has measurements 12, 15, 19 and group B has 7, 9, 14, 16. To test whether A tends to give larger values, use a permutation test with test statistic equal to the mean of group A (equivalently, the difference in group means). Under the null hypothesis that group labels are exchangeable, all $\binom73=35$ ways of choosing which three of the seven values form group A are equally likely. What is the exact one-sided p-value, the probability under relabeling of a group-A mean at least as large as the observed one? Give a reduced fraction.

• combinations
• hypothesis testing
• permutations

Source: Original problem written for AxiomIQ. The permutation (randomization) test goes back to R. A. Fisher and E. J. G. Pitman. Statement written for AxiomIQ.