Database is slow once in a while
Yes, statspack is an easy free way to go. First thing to look at is the top 5 timed events. Unfortunately statspack won't tell you the problem for specific sql statements. To see where and how particular sql statements are spending their time, you need ASH. A graphical interface to ASH along with the collection of ASH (ie no perf pack license needed)  is available with WASH.
http://www.oraclerealworld.com/web-ash-w-ash/
I'd recommend lab128 which has a 2 day free trial
http://www.lab128.com/lab128_download.html
Lab128 can collect ASH itself or optionally use the ASH collection from the performance pack.
One you have on of those running, see where you are spending time - CPU, I/O, Locks or other stuff.
In both the above tools you can see where individual SQL spend time to help you distinguish a problem in one SQL vs loosing that SQLs problems in the overall stats of the database.