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.
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