True or False?
The statement is false. When the exchange rate is fixed, equilibrium in the small country depends on the intersection of its IS curve with the real interest rate line. A change in the world interest rate will thus necessarily involve a change in the small country's output, since the IS curve is negatively sloped. So insulation from foreign real shocks does not occur. A real shock in the small country shifts its IS curve. Since equilibrium is determined by the intersection of IS and the real interest rate line a real shock in the small country must lead to a change in its output and ultimately its price level. So a fixed exchange rate does not insulate a small open economy from domestic real shocks either.
There is a possibility that fixing the exchange rate may insulate the small country's price level from big-country real shocks in the long run. If the equilibrating change in the price level in the big country happens to move the small country's real exchange by just the right amount, the small country's price level could end up unchanged (along with, of course, the nominal exchange rate) in the new equilibrium compared to the pre-shock situation. This can be seen from the definition of the real exchange rate.