1. A blood analyzer comprising: a blood specimen supplying portion for supplying a blood specimen; a sample preparation portion for preparing a measurement sample without using a fluorescence-labeled antibody by mixing the blood specimen supplied from the blood specimen supplying portion, a hemolyzing agent, and a fluorescent dye that stains nucleic acid; a light source for irradiating light onto the measurement sample prepared by the sample preparation portion; a first detector for detecting fluorescence emitted from the measurement sample irradiated with light by the light source; a second detector for detecting scattered light emitted from the measurement sample irradiated with light by the light source; an information processing portion for obtaining an indicator representing a particle size distribution of fluorescence intensity of lymphocytes based on intensity of fluorescence detected by the first detector and intensity of scattered light detected by the second detector, and obtaining information regarding a ratio of a B-lymphocyte count to a T-lymphocyte count based on the obtained indicator representing the particle size distribution of fluorescence intensity of lymphocytes; and an output portion for outputting the information regarding the ratio of the B-lymphocyte count to the T-lymphocyte count obtained by the information processing portion.