Step 1 :Determine the direction of equilibrium shift due to a decrease in the equilibrium constant.
Step 2 :The equilibrium constant (K) of a reaction is a measure of the ratio of the concentrations of the products to the reactants at equilibrium.
Step 3 :If the equilibrium constant decreases, it means that the ratio of the concentrations of the products to the reactants is decreasing.
Step 4 :This implies that the reaction is shifting in the direction of the reactants, or to the left.
Step 5 :Therefore, a decrease in the equilibrium constant due to a temperature change would cause the equilibrium to shift to the left.
Step 6 :Final Answer: The temperature change causes the equilibrium to shift to the \(\boxed{left}\).