Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and higher order thinking through the same mathematical activities--an aim which requires empirical examination. For empirically valid hybrid task design, evidence is required about the nature of the interrelatedness of content-related and higher order thinking. In this article, we choose the example of statistical thinking and critical thinking for exploring the interrelatedness of these different modes of thinking when solving hybrid tasks. Even if theories about statistical thinking and critical thinking have so far followed almost separate strands, there are commonalities at the theoretical level, which facilitate hybrid task design. We report an empirical study, in which a bottom-up analysis of thinking-aloud interviews with adult learners around solution processes of hybrid tasks affords insight into how these modes of thinking may interact when solving such tasks. The results show that the tasks did evoke both statistical thinking and critical thinking: Both modes of thinking entered in an interplay in which we observed instances of mutual support of both modes of thinking, but also cases in which a strong focus on statistical thinking or critical thinking appeared to impede the other mode of thinking, respectively. The findings can inform the further development of hybrid tasks: Based on the observations, the task format can be enriched with specific reflective stimuli intended to support a fruitful interplay of statistical thinking and critical thinking.