Do you get a better performance using premier gasoline (Octane number 93) for your compact car?

Yes

Explanation:

As we know that octane number resist the engine from knocking. If knocking can prevent that automatically the performance of engine will increases. If octane number is 100 then it means that knocking tendency in the engine is zero. So higher the octane number better will the performance of the engine.

Generally octane number is 87 but for premier gasoline is 92 or 93.

So we can say that if octane number is 93 then car will give better performance