the autority to review the decision of lower courts and decide if the laws properly applied in a particular case is called

The correct answer is Appellate Jurisdiction. Indeed, when a case has been tried in a lower court and one of the parties (either the defendant or the prosecution) are dissatisfied with the sentence. They can the decision and a higher court with judges who have more experience and power than the judges of the lower courts will review the decision and decide if all the laws and procedures were properly respected and shoudl that not be the case they would have the authority to nullify such decision.

The autority to review the decision of lower courts and decide if the laws properly applied in a particular case is called Judicial Review. Its purpose is to ensure the Tribunal compelled with the law in reaching itsdecision. The Court often deals with determining whether the Tribunal had the authority to make the decision it made or whether the Tribunal properly exercised that authority. The Judicial Review Procedure Act provides that a court possess the power to set aside a decision for an error of law, an absence of evidence or where the exercise of the power is invalid or unauthorized.