Steering

95bluestreak

Hey everyone. I'm new to this site. I spend most of my "forum" time on the Ford F-150 site trying to keep my 1995 truck running.
My wife drives a 2010 370Z automatic, and it has 38000 miles. I took it to Discount Tire for new rear tires last Friday, and on the way home noticed that the steering feels "mushy" or "loose" - hard to control. It kinda feels like driving an old car with loose steering. The road surface makes a difference, with rough roads causing more trouble. I checked to be sure that all of the wheels are securely tightened. They had inflated all of the tires to 38lbs, so I let some air out down to 32lbs. That helped some.
We were leaving on a trip so didn't take it back to Discount Tire yet, and it is an hour away, so a pain to take back. My question for all of you is what about replacing the rear tires could cause the steering to change? By the way, replaced the factory Yokohama's with Yokohama YK580 245/45R18's.
Thanks for any ideas.