Vertical velocity dispersion (σ_W) of hot-Jupiter host samples (orange dashed lines) vs. those of matched field-star control samples (black histograms) for the updated HS19 sample. The shaded regions and dashed black line indicate the 68%–95%–99.7% confidence intervals and median of the field-star histograms. The gray dashed lines indicate the σ_W threshold at which the relative age difference from the field-star median reaches 50%. The σ_W values for the HJ sample and the field-star median are given in the upper right corners in orange and black respectively. Panels (a) and (b): the whole updated HS19 sample, without and with a distance cut of d  <  600 pc. Panels (c) and (d): ground-based transit (TG) and radial velocity (RV) hosts in the updated HS19 sample with d  <  600 pc.