Step 1: Recall the meaning
In the rate law \(r=k[A]^n\), \(k\) is the proportionality constant. It does not depend on concentration but changes with temperature.
Step 2: Check the options
(A), (B) and (C) are true.
(D) is false: for the same concentrations a larger \(k\) gives a larger rate, so the reaction is faster.
Final Answer:
Statement (D) is not true, option (D).
\[ \boxed{\text{(D)}} \]