© 2016 authors. Published by the American Physical Society. An updated measurement of the single top quark production cross section is presented using the full data set collected by the Collider Detector at Fermilab (CDF), corresponding to 9.5 fb-1 of integrated luminosity from proton-antiproton collisions at 1.96 TeV center-of-mass energy. The events selected contain an imbalance in the total transverse momentum, jets identified as containing b quarks, and no identified leptons. The sum of the s- and t-channel single top quark cross sections is measured to be 3.53-1.16+1.25 pb and a lower limit on the magnitude of the top-to-bottom quark coupling, |Vtb| of 0.63, is obtained at the 95% credibility level. These measurements are combined with previously reported CDF results obtained from events with an imbalance in total transverse momentum, jets identified as originating from b quarks, and one identified lepton. The combined cross section is measured to be 3.02-0.48+0.49 pb and a lower limit on |Vtb| of 0.84 is obtained at the 95% credibility level.