Both are okay, but each one means something different. The first one means that there are some programs about 15-year-old children. The second one means that there are some programs about one 15-year-old child.
Both are okay, but each one means something different. The first one means that there are some programs about 15-year-old children. The second one means that there are some programs about one* 15-year-old child.
Except when it is a generic singular as in 'the female of the species is more deadly than the male'. The generic usage is less common, but acceptable (especially in formal contexts:
'The ten-year-old is generally obedient, but the fifteen-year-old is less so. In my study, 100 ten-year-olds were...'
Both are okay, but each one means something different. The first one means that there are some programs about 15-year-old children. The second one means that there are some programs about one 15-year-old child.
Your interpretation of the second is possible - if we are referring to a particular child. If we aren't, then I would take it to mean the same as the first sentence.