Aren't interest rates reduced to stimulate a struggling economy, and increased if economy improving?

Right. If interest rates are increased, that's a sign of a stronger economy and the market might go up in response. On the other hand, traders might decide the Fed is mistaken, the economy is not in fact stronger, and they'll react to the higher interest rates by taking fewer loans and the market will go down.

Basically, the change is already priced-in and you shouldn't worry about timing the market. Buy and hold.

Interest rates go up when the economy is improving.

Oops. That's what I meant to say: s/reduce/increase/