A statistical hypothesis about Earth's magnetic field is tested against paleomagnetism by combining it with the present field to estimate mean paleointensity. The estimate uses the satellite era geomagnetic multipole power spectrum Rn, which gives the mean square magnetic induction represented by spherical harmonics of degree n averaged over the sphere of radius a = 6371.2 km. The hypothesis asserts that low-degree multipole powers of the core source field, Rnc, are distributed as chi-square with 2n + 1 degrees of freedom and theoretical expectation values {Rnc} = K(n + 1/2)<n(n + 1)>-1(c/a)2n + 4, where c is the 3480 km radius of Earth's core. The implied field is usually mainly dipolar and can be primarily axial. Amplitude K is estimated by fitting theoretical to observational spectra of degrees 1--12. The resulting calibrated expectation spectrum is summed through degree 12 to estimate expected square intensity {F2}. This sum also estimates mean square paleointensity, averaged over geologic time as well as the sphere, in so far as the present field spectrum is a fair sample of that generated in the past by core geodynamic processes. Previously, we excluded dominant degrees 1 and 2 from the fit, but not the sum, to "predict" mean paleointensity from the 1980 Magsat nondipole field. The new estimate fits all Rn of degrees 1--12 self-consistently and yields {F2} = (37.3 ¿ 4.3 ¿T)2. Expected paleointensity {F} is about 34.4 ¿ 4.9 ¿T; expected virtual axial dipole moment is about (6.51 ¿ 0.94) ¿ 1022 Am2. These estimates are within the range of published paleomagnetic determinations of mean paleointensity; therefore the statistical hypothesis passes this test.