Listening effort (LE) is critical to understanding speech perception in acoustically challenging environments. EEG alpha power has emerged as a potential neural correlate of LE. However, the magnitude and direction of the relationship between acoustic challenge and alpha power has been inconsistent in the literature. In the current study, a secondary data analysis of Silcox and Payne (2021), we examine the broadband 1/f-like exponent and offset of the EEG power spectrum as measures of aperiodic neural activity during effortful speech perception and the influence of this aperiodic activity on reliable estimation of periodic (i.e., alpha) neural activity. EEG was continuously recorded during sentence listening and the broadband (1-40 Hz) EEG power spectrum was computed for each participant for quiet and noise trials separately. Using the specparam algorithm, we decomposed the power spectrum into both aperiodic and periodic components and found that broadband aperiodic activity was sensitive to background noise during speech perception and additionally impacted the measurement of noise-induced changes on alpha oscillations. We discuss the implications of these results for the LE and neural speech processing literatures.