There is resurging interest in the engineering education community in entrepreneurial activities and the development of an entrepreneurial mindset (EM). According to the KERN Entrepreneurship Education Network, facets of an EM include curiosity, an emphasis on creating value, and the ability to make connections. While extracurricular activities are the primary mechanism by which this topic has been introduced to engineering students in the past, it is beginning to show up in more formal ways. The literature includes examples many of how to promote entrepreneurship and an EM in traditional project-based courses engineering students take (senior design, etc.); but there are fewer examples and best practices for cultivating an EM in a fundamental engineering course-namely engineering statistics. Project-based learning (PBL) is a pedagogical approach that involves active learning directed at investigating and solving complex, real-world problems- and it is an approach that is underutilized in math-intensive engineering courses. The purpose of this study is to demonstrate how PBL can be integrated into an undergraduate engineering statistics course to promote an entrepreneurial mindset and investigate its impact on student learning. Six teams of engineering students in a 200-level engineering statistics courses responded to the challenge of presenting "A World Without Statistics". Teams were given liberty to choose any topic of interest and received funding to support their idea. The resulting projects creatively conveyed what the world would be like without statistics using a myriad of topics: sports, resilient infrastructure, online data, robotics, artificial intelligence, and manufacturing. Evidence suggest that curiosity, an emphasis on understanding the value of statistics, and the ability to make connections were critical to each team's success. This paper provides an overview of the assignment, and examples of students' work. Such insights have the potential to not only influence the way we cultivate an entrepreneurial mindset in fundamental engineering courses, but also shed light on innovative ways to integrate other multi-faceted topics in engineering education.