I'm running into issues trying to figure out what type of test to use and whether two tailed or one tailed in different scenarios. How do you determine what to do in the scenarios presented? For example, the following problem I'm trying to do I'm running into the exact issue stated above.
"A battery manufacturer randomly selects $100$ nickel plates for test cells, cycles them a number of times, and determines that $14$ of the plates have blistered. Does this provide compelling evidence for concluding that more than $10\%$ of all plates blister under such circumstances? State and test the appropriate hypotheses using a significance level of $\alpha=0.05$."
Take the example for instance and immediately what I think of is that it is one tailed simply because there's nothing being compared. For the hypothesis however I'm struggling to figure out which one to use. For this example in particular I imagine the following would work since to my understanding it uses a normal distribution.
$z=\dfrac{\overline{x}-\mu_0}{s/\sqrt{n}}$
Except then I run into issues where I'm unsure of what to do since there is no mean or standard deviation stated in the problem.
Could someone give me some hints on how to understand what type of test I should use in different scenarios and if I am using the wrong formula for the scenario above?
Use the test $H_0: p=0.1(\equiv 10\%)$ against $H_1:p>0.1(\equiv 10\%)$. Simple binomial test.