Right, this is interesting.
So if I wanted to establish whether an old family rumor was correct or not (my great-great-grandmother was apparently Jewish) is this something that can be determined with a DNA test? Or do I need to try to find whatever family records might exist and determine it that way?
How does one know if they are Jewish?
Through family history or genealogy. I find no Jewish roots and have worked many lines going way back for over 10 years now. I've found possibly one Native American (can't be proven) and no black, doesn't mean anything in particular.
This new DNA testing might shed further light on it, as my mainly English/Scottish ancestors had to have migrated from somewhere, plus there's about 1/4 German. Since I don't understand the terminology and interpretation of results, DNA can be a wonderful tool or a slippery slope. For me to believe any of it requires blind faith in the science.
I don’t think it would work in your case since it tracks a gene on the Y chromosone. It would therefore only track the male line.
Bar Mitzvah.
If she's in maternal line, go here and order your kit.
I did a while ago (I checked my Y-chromosome) and found out that--although a Jew--my Y-chromosome was pure Celtic. My father's line comes from a Mahoney, a Pickering or a Nicholson. How long ago, I don't know.
“old family rumors...determined with a DNA test?”
The presence of certain genes might confirm something, but the absence would not necessarily prove anything. Since genes come in pairs, and only one is passed to the offspring, there is a 50/50 chance of the gene not being passed on, unless both chromosomes had the target gene. By all means search family records, old census data, etc.