Using p value mathod in hypothesis testing

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As we know there are two way test a hypothesis. One is critical value method and the other is p value method. I've discovered that its very difficult to calculate p value in hand besides there are some statistical tools to calculate p value instead. But my professor will not let me use statistical tool. If I follow critical value method instead to solve problems more efficiently and easily will it be wrong? As there are two methods available. And is there any shortcut way to calculate the p value in both t and z test please help me to find out. Thank you and apologize for making the this long.