How can I delay the app loading to show the splash screen for longer?
See the above discussion of why you probably should not delay your app load in this way. But if you happen to have a scenario where sleeping for short duration would be preferable to the overhead of switching out a view, use NSThread's sleepForTimeIntervale instead of sleep(). It's more framework friendly and you have more granular control over the sleep time:
[NSThread sleepForTimeInterval:0.75]