Hi, I was told by a home inspector that in old house with knob and tube wiring, you can install a GFCI outlet without the ground, and it should trip. I did this and when I tested it, the power did not cut off. Is there something else or was he incorrect? Thank you.

It should trip.. Are you sure you wired in the supply side, not the load side?

How did you test it?
A plug-in tester will not work without a ground. The only accurate GFI test is the button on the device.
If you are using the button on the device and it is not working the GFI is either wired wrong or defective.

I used a plug in tester, using a radio and the test button, it tripped correctly. Thank you.