As Art has noted, there has been a significant Jewish population in Palestine since the Crusades.

It's hard to say whether there were more Jews or more Arabs in Palestine at the beginning of the last century - statistics are inconclusive. While both Arab and Jewish sources quote British census statistics of 1931 to support their own claims of demographic dominance, there are many different sources of information, some of which conflict with each other.

this site has a lot of interesting information about statistical records of population and immigration by Jews and Arabs into the area, and which groups (eg Bedouins) may have been excluded:
The population of Palestine prior to 1948

It quotes a number of sources including the Ottoman census of 1893, various British census figures, the Encyclopedia of the Palestinians, and information collected since the mid 1800s by various officials. It also has links to a number of other sites which analyse the question of demographic dominance as well.

It's worth a look.