I was in this position last week with my Explorer.
I am guessing that your F150 is similar to my Explorer.
If so, here is what you need to do.
On your rear diff, there is a metal tag. It will have a code. (few digits)
There is also a code for the gears on the tag inside the door.
For example..my code in the door is D4...
Then you take that code and find the correct translation with a chart.
Now I can not say for sure if your chart would work just like mine..(For the Explorer)....but to give you an idea what you are looking for, I will post mine....
41 - Conventional - 3200 lb. Capacity - 3.27 Ratio
45 - Conventional - 3200 lb. Capacity - 3.55 Ratio
D4 - Limited Slip - 3200 lb. Capacity - 3.73 Ratio
46 - Conventional - 3200 lb. Capacity - 3.73 Ratio
D1 - Limited Slip - 3200 lb. Capacity - 3.27 Ratio
42 - Conventional - 3200 lb. Capacity - 4.10 Ratio
D2 - Limited Slip - 3200 lb. Capacity - 4.10 Ratio
As you can see, my D4 gear ratio is 3.73....