I don't think so

1. Literally, I don't believe that to be true. A: "Is Tom finished with that report yet?" B: "I don't think so, no." I don't think so, but let me check. Nope, Andrew's not here yet. A: "Somebody said we have a quiz today in Geometry!" B: "No, I don't think so. If we did, I would have written that down."

2. Used rhetorically to refuse, decline, or reject something. A: "Come on, be a pal and let me copy your homework?" B: "I don't think so, Tonya. Do your own work." Loan your deadbeat brother money? Ha, I don't think so! Yeah, I don't think so. If you're gonna sneak out and go to that party, that's fine, but I'm not getting in trouble covering for you!

I don't think so

I don’t agree with what was just stated, either by myself or by someone else. Generally pronounced with a marked emphasis on think, this twentieth-century expression started out as I don’t think, with the emphasis on don’t, in the nineteenth century. Dickens had it in Pickwick Papers (1837): “‘Amiably disposed . . . , ‘I don’t think,’ resumed Mr. Weller, in a tone of moral reproof.” More recently, the headline of an online story concerning former vice president Al Gore read, “Gore Sexual Assault? I Don’t Think So” (June 28, 2010). An online finance report posted December 17, 2008, was headed, “Buy Adobe now? I don’t think so.” A slangy one-word synonym used in the same way is not, which became very popular from the late 1980s on. It actually originated a century or so earlier; J. E. Lighter cites the Princeton Tiger of March 30, 1893: “An Historical Parallel—Not.” It reappeared on the television show Saturday Night Live and in the film Wayne’s World (1992), but may again be dying out.