# Math Help - hypothesis testing

1. ## hypothesis testing

A commuter railroad advertises that their trains have an average on-time 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 on-time 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.

2. 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 $\hat p=.83$
There seems to be 53 of the 64 trains on time, in this sample.

I would go with $H_0=.85" alt="H_0=.85" /> vs. $H_a\ne .85" alt="H_a\ne .85" />

But one can argue (mainly after looking at the data, which is cheating), that $H_a< .85" alt="H_a< .85" />

The test stat would be ${\hat p- .85\over \sqrt{(.85)(.15)\over 64}}$

Another weird thing is the statement that the st deviation is 5 percent.

I did calculate the approximate st deviation as $\sqrt{(.85)(.15)\over 64}=.0446329$