This is the most common way for professors to want you to deal with hypothesis testing of proportions. It's not as easy as just using the 1-sample proportion test on your calculator -- which is pure plug-and-chug -- but it's favored by teachers because it's a nice compromise between the retro method of z-tables and the no-thinking world of letting the calculator do everything for you.
Testing Claims About Proportions Using Critical Z-Values
This is the "other way" to test a hypothesis about a proportion: most of the steps of the process are the same as using the P-value method, except instead of converting the z-value of your sample to a P-value (probability), you instead compare it to the cutoff critical z-value for the desired level of confidence.
Testing Claims About Proportions on Calculator
This is the easiest method to test a hypothesis about a proportion: just go into the stats menu on your calculator, select the one-sample proportion test, and enter numbers directly from the word problem. You'll still have to know what a P-value and z-value mean, since that's what the calculator spits out, but at least you won't have to memorize any formulas!
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)