Improving students' understanding of the nature of experimental physics is often an explicit or implicit goal of undergraduate laboratory physics courses. However, lab activities in traditional lab courses are typically characterized by highly structured, guided labs that often do not require or encourage students to engage authentically in the process of experimental physics. Alternatively, open-ended laboratory activities can provide a more authentic learning environment by, for example, allowing students to exercise greater autonomy in what and how physical phenomena are investigated. Engaging in authentic practices may be a critical part of improving students' beliefs around the nature of experimental physics. Here, we investigate the impact of open-ended activities in undergraduate lab courses on students' epistemologies and expectations about the nature of experimental physics, as well as their confidence and affect, as measured by the Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS). Using a national data set of student responses to the E-CLASS, we find that the inclusion of some open-ended lab activities in a lab course correlates with more expertlike postinstruction responses relative to courses that include only traditional guided lab activities. This finding holds when examining postinstruction E-CLASS scores while controlling for the variance associated with preinstruction scores, course level, student major, and student gender.