Yes, you can change the privacy of you status as well as you can customize it too, you can write your own status that you like.
Go to settings option , account settings then tap Privacy and select "Status" there you can choose any of the options from: Everyone, My contacts, Nobody.
If you want to change your status select status option, there you will see one textbox below "your current status" heading ,there you can write new status that you want.
