Answer
The brightness will decrease.
Work Step by Step
When the switch is closed, the resistor is added in parallel. This lowers the equivalent resistance of the circuit, so the current that the battery supplies will increase.
We are told that this is a real battery with nonnegligible internal resistance, so the extra current will lower the terminal voltage (page 833). The bulb now has a lower voltage drop across it, so it will become (slightly) dimmer.
