Problem
We have a Dropdown in InfoPath which is populated from external data source (SharePoint List. e.g. TimeSheet List having fields ProjectName, %Complete and Type. Dropdown is showing Project Names). We want to populate infopath field (Type) from SharePoint based on selected Project in dropdown.
Solution
I suppose you have already Filled Dropdown from Timesheet List and or applied filtering if required, If not, you can follow my post How to Filter Infopath Dropdown.
Select the Project dropdown that we created in previous article and from the "Home" ribbon, select Add Rule->This Field Changes -> Set a Field's Value option as shown in the below image.