Product review (5 stars): See if this will this fit your machine.
I am posting this to help you decide if this item will fit your washing machine before you order it.  I had trouble figuring that out when I was ordering so allow me to help.  I cannot attest to the functionality of this item because I just received it today.  Please read other reviews for that.

I own a Roper Model #RTW4516FW.  This is the same as the Amana Model #NTW4516FW.  They are both made by Whirlpool.

To install this item, you must remove the top cap on the agitator.  You won't need any tools for this.  It pops right off.  The Dispenser then fits down and snaps into place inside the agitator.  Measure the inside dimensions.

From the inside edge of the shoulder to the bottom of the dispenser is 4-5/8 inches.  See picture.  With the original cap removed from the agitator, make sure you have enough depth for the dispenser to fit.  Mine is a close fit.  The diameter of the dispenser is a little over 3-1/2 inches.  There are tabbed lines that hold the dispenser in the agitator.  I can't get an exact measurement but the hole in my agitator is barely under 3-5/8 inches and it fits perfectly snug.

The dispenser I received is a Whirlpool Factory Certified Part and Made in the USA.