Why does this "Cannot create property text on String" error happen?

I have three text boxes(textBox1, textBox2, textBox3) on stage that I want a single message to be passed onto each text box but can't seem to get it to work. The code below keeps getting this error message: "Cannot create property text on String." How do I make "textBox" not a string.

var textBoxes:Array = new Array();

var winnerText:String = "You Won";

var randomNum:Number = Math.ceil(Math.random() * 3);
var i:int;
var n:int;
for (i = 1; i <= 3; i++)
{
textBoxes.push("textBox" + i);
n = i-1;
textBoxes.text = winnerText;
}