How to test a hypothesis about the mean based on an assumed normal distribution? 
The entrance onto a major bridge in New York City was engineered to accommodate
  an average of $3800$ vehicles per hour. However, a random sample of nine observations
  gives an average of $4045.9$ vehicles per hour with a standard deviation of $201.3$
  vehicles. Use a $5\%$ significance level to test the claim that the true average number
  of vehicles per hour is more than $3800$. Assume that the number of vehicles per
  hour is normally distributed.

I'm not sure on how to start. Can you please help?
 A: Your first question is to determine whether you are using the normal distribution or the $t$-distribution.  These are possible sampling distributions for your test statistic.  If you are estimating the standard deviation from your data, there is some uncertainty about the true value of the SD.  You need to take that additional uncertainty into account.  The $t$-distribution, with its higher variance / fatter tails, does this for you.  You should use the $t$-distribution here.  
Next we need to determine the value for $n$.  It is not the size of your population.  Your population is assumed to be infinite.  Instead, it is the size of your sample.  From the problem description, I gather your $n=9$.
$$
t = \frac{\bar x-\mu_0}{\frac{s}{\sqrt n}}
$$
Lastly, the numerator for the one-sample $t$-test (in the formula above) lists two values.  You need to figure out what those refer to and plug in the appropriate numbers from your problem description.  Then (with a little arithmetic), you will be done.  
