Wire hot with light switch turned off
Installing a ceiling fan in 40 year old house. I removed the old ceiling fixture - in addition to black hot and white neutral attached to fixture, there is a black wire attached to a white wire in the box. This light is controlled by only one switch. With the wall switch off, my tester light is very bright touching the hot wire and the metal box - and the test light comes on dim when I touch the hot and neutral with the tester light. The circuit includes two rooms, each with a switched ceiling light and 6 wall outlets. Is there something wrong here?