We present a measurement of the CP-violating parameter betas using approximately 6500 $BsJpsiPhi$ decays reconstructed with the CDF,II detector in a sample of $pbar p$ collisions at $sqrt{s}=1.96$ TeV corresponding to 5.2 fb$^{-1}$ integrated luminosity produced by the Tevatron Collider at Fermilab. We find the CP-violating phase to be within the range $betas in [0.02, 0.52] cup [1.08, 1.55]$ at 68% confidence level where the coverage property of the quoted interval is guaranteed using a frequentist statistical analysis. This result is in agreement with the standard model expectation at the level of about one Gaussian standard deviation. We consider the inclusion of a potential $S$-wave contribution to the $Bsto J/psi K^+K^-$ final state which is found to be negligible over the mass interval $1.009 < m(K^+K^-)<1.028 gevcc$. Assuming the standard model prediction for the CP-violating phase betas, we find the Bs decay width difference to be $deltaG = 0.075 pm 0.035,textrm{(stat)} pm 0.006,textrm{(syst)} ps$. We also present the most precise measurements of the Bs mean lifetime $tau(Bs) = 1.529 pm 0.025,textrm{(stat)} pm 0.012,textrm{(syst)}$ ps, the polarization fractions $|A_0(0)|^2 = 0.524 pm 0.013,textrm{(stat)} pm 0.015,textrm{(syst)}$ and $|A_{parallel}(0)|^2 = 0.231 pm 0.014,textrm{(stat)} pm 0.015,textrm{(syst)}$, as well as the strong phase $delta_{perp}= 2.95 pm 0.64,textrm{(stat)} pm 0.07,textrm{(syst)} textrm{rad}$. In addition, we report an alternative Bayesian analysis that gives results consistent with the frequentist approach.
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