Alternators dont just provide voltage they provide current. The alternator should charge the battery at about 14 volts. Or just slightly above. Increase the load on the system until it meets the amp rating of the alternator. The voltage should read battery voltage or about 12 volts. If at the alternators amp rating, the voltage is lower than 12, replace the alternator. Of course, the first thing you always check are the connections. Unwanted resistance is the most common cause of electrical failure. Usually this is in the form of a bad connection or corrosion. Corrosion equals a voltage drop which would cause a slow crank even with a good battery. I would check the voltage drop between the battery post and cable clamp. Then from the cable clamp to the cable directly after the clamp. Then check for a poor ground connection to the engine block.