This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning environment, and what role processes of data production play in their investigations. The study outlines aspects of students’ informal understanding of hypothesis testing. It shows how students with no formal education can follow the logic that a small difference in samples can be the effect of randomness, while a large difference implies a real difference in the underlying process. The students distinguish the mode and the size of differences in frequencies as signals in data and used these signals to give data-based reasons in processes of informal hypothesis testing. The study also highlights the role of data production and points to a need for further research on the role of data production in an informal approach to the teaching and learning of statistical inference. First published December 2020 at Statistics Education Research Journal: Archives