A decrease in the globally averaged low level cloud cover, deduced from the ISCCP infrared data, as the cosmic ray intensity decreased during the solar cycle 22 was observed by two groups. The groups went on to hypothesize that the decrease in ionization due to cosmic rays causes the decrease in cloud cover, thereby explaining a large part of the currently observed global warming. We have examined this hypothesis to look for evidence to corroborate it. None has been found and so our conclusions are to doubt it. From the absence of corroborative evidence, we estimate that less than 23%, at the 95% confidence level, of the 11 year cycle change in the globally averaged cloud cover observed in solar cycle 22 is due to the change in the rate of ionization from the solar modulation of cosmic rays.