We were not a minority in the Nineveh Plains and in the Duhok province. We were no doubt the majority. Centuries later with continued genocides and ethnic cleansing of-course we have become a minority on our indigenous lands.
Assyrians were a large minority across the whole state, according to the information i could find they were likely the plurality or majority across Duhok and Nineveh but it includes many Arab and Kurdish areas as well