Yes, you can downsize the purple hat, it's written for very thin yarn. The pattern repeat is a multiple of 12 so you can use 60 sts rather than 64. If you get 3 sts per inch with your yarn on size 11s that would make it about 20" around. The 11 sts/4" on the label gauge is just to show that it's a bulky/chunky yarn.
sue- knitting heretic