Age-related cochlear synaptopathy (CS) has been shown to occur in rodents with minimal noise exposure, and has been hypothesized to play a crucial role in age-related hearing declines in humans. It is not known to what extent age-related CS occurs in humans, and how it affects the coding of supra-threshold sounds and speech in noise. Because in rodents CS affects mainly low- and medium-spontaneous rate (L/M-SR) auditory-nerve fibers with rate-level functions covering medium-high levels, it should lead to greater deficits in the processing of sounds at high than at low stimulus levels. In this cross-sectional study the performance of 102 listeners across the age range (34 young, 34 middle-aged, 34 older) was assessed in a set of psychophysical temporal processing and speech reception in noise tests at both low, and high stimulus levels. Mixed-effect multiple regression models were used to estimate the effects of age while partialing out effects of audiometric thresholds, lifetime noise exposure, cognitive abilities (assessed with additional tests), and musical experience. Age was independently associated with performance deficits on several tests. However, only for one out of 13 tests were age effects credibly larger at the high compared to the low stimulus level. Overall these results do not provide much evidence that age-related CS, to the extent to which it may occur in humans according to the rodent model of greater L/M-SR synaptic loss, has substantial effects on psychophysical measures of auditory temporal processing or on speech reception in noise.