
hypothesis testing
. Im stumped basically on how to find the critical value. please help
A commuter railroad advertises that their trains have an average ontime arrival record of exactly 85 percent. A transportation analyst conducts a study to determine if this claim is true. He checks arrival performance for a sample of 64 commuter trains and finds that the average ontime arrival rate is 83 percent. It is known that the population standard deviation is 5 percent. Test the hypothesis that the commuter railroad’s claim is true at = 0.05.
a. State the null and alternative hypothesis.
b. Determine the critical value of the statistic.
c. Write the decision rule.
d. Calculate the sample test statistic.
e. Perform the test.
f. Write a conclusion based on your answer to part e.

I would think that we wnat to test a proportion here.
I'm not sure if they want to disprove the claim or prove it's too high.
P is the true proportion of trains that arrive on time.
Based on n=64 and what seems to be an sample proportion of successes $\displaystyle \hat p=.83$
There seems to be 53 of the 64 trains on time, in this sample.
I would go with $\displaystyle H_0:p=.85$ vs. $\displaystyle H_a:p\ne .85$
But one can argue (mainly after looking at the data, which is cheating), that $\displaystyle H_a:p< .85$
The test stat would be $\displaystyle {\hat p .85\over \sqrt{(.85)(.15)\over 64}}$
Another weird thing is the statement that the st deviation is 5 percent.
I did calculate the approximate st deviation as $\displaystyle \sqrt{(.85)(.15)\over 64}=.0446329$