Writer:

A writer is a person who uses written words in various styles and techniques to communicate their ideas. Writers produce various forms of literary art and creative writing such as novels, short stories, poetry, plays, screenplays, and essays as well as various reports and news articles that may be of interest to the public.

Composer:

A Composer is a person who writes music, especially as a professional occupation. It including vocal music(for a singer or choir), instrumental music, electronic music, and music which combines different forms.Statesmen:

A statesman or stateswoman is usually a politician, diplomat or another notable public figure who has had a long and respected career at the national or international level.

So it already explained, statesmen is totally different from Writer & Composer. Because He/She relates to the government, whereas writer & composer deals with the lyrical world, they both are in the same bowl with the different field.