Used when you believe something should certainly happen, without a doubt. 'This printer will work now, right?' 'I should hope so.'
Pro Tip 2/3
Subtle Force
It implies a strong expectation, almost as if you're insisting on the outcome. 'Your brother will pay back the money?' 'I should hope so.'
Pro Tip 3/3
Mild Frustration
Can carry a tone of mild irritation or frustration when the outcome is expected but not yet seen. 'Has he cleaned his room yet?' 'I should hope so, after all the nagging.'