Does a new chain slipping on an old cassette's cogs prove the cassette's teeth are wo

I put a new chain (Bell Links 500 - a cheap chain from Walmart but they've worked for me before) on (I rotate chains monthly). It slips on the cogs I use more frequently (which happen to be the larger ones). The cassette is the Shimano with the 34-tooth cog. I wish I had a good way to measure...