Testing Claims (Hypotheses) About Proportions
Testing Claims About Proportions Using P-Values
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!