We report new continuum observations of 14 z ～ 6 quasars at 250 GHz and 14 quasars at 1.4 GHz. We summarize all recent millimeter and radio observations of the sample of the 33 quasars known with 5.71 ≤ z ≤ 6.43 and present a study of the rest-frame far-infrared (FIR) properties of this sample. These quasars were observed with the Max Planck Millimeter Bolometer Array (MAMBO) at 250 GHz with mJy sensitivity, and 30% of them were detected. We also recover the average 250 GHz flux density of the MAMBO undetected sources at 4 σ by stacking the on-source measurements. The derived mean radio-to-UV spectral energy distributions (SEDs) of the full sample and the 250 GHz nondetections show no significant differences from lower redshift optical quasars. Obvious FIR excesses are seen in the individual SEDs of the strong 250 GHz detections, with FIR-to-radio emission ratios consistent with those of typical star-forming galaxies. Most 250 GHz-detected sources follow the L_(FIR)-L_(bol) relationship derived from a sample of local IR-luminous quasars (L_(IR) > 10~(12) L_☉), while the average L_(FIR)/L_(bol) ratio of the nondetections is consistent with that of the optically selected PG quasars. The MAMBO detections also tend to have weaker Lyα emission than the nondetected sources. We discuss possible FIR dust-heating sources and critically assess the possibility of active star formation in the host galaxies of the z ～ 6 quasars. The average star formation rate of the MAMBO nondetections is likely to be less than a few hundred M_☉yr~(-1), but in the strong detections, the host galaxy star formation is probably at a rate of approx>10~3 M_☉ yr~(-1), which dominates the FIR dust heating.
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