How to hide time from the date display? In a view using Articles and Blog posts sorted by recent post date, I'm using [Content: Post date] and I would like to display (as a column on the display) as only the date and not the time, i.e. 2016/04/08. 

I merely wish to alter what data Drupal is displaying, not the data it is collecting.

How can I apply this date format to the field in the view?

In Home>Administration>Date and Time, I can add new date type but all 19 of the options include displays of time.
There should also be a Formats tab at the top of that page. Here you can add additional formatting (like date or time only formats). After saving the format, go back to the first page and now you can select your newly created format as an option.