Imply and Infer
From Pairs Of Words in Vocabulary

It is a common error to use infer for imply. A writer or speaker implies what his reader or listener infers. The difference is illustrated thus by Sir Alan Herbert:

If you see a man staggering along the road you may infer that he is drunk, without saying a word; but if you say "Had one too many?" you do not infer but imply that he is drunk.