The director of the Financial Aid Office at a particular public school claims that the average amount of money that students receive per semester is $4250. A sample of 36 students' award letters has a mean of $4500 with a known population standard deviation of $430. Is there enough evidence to support the directors claim at = 0.05? (10 pts)

1. Identify the null hypothesis and the alternative hypothesis and identify the claim.
2. Find the critical value(s).
3. Compute the test statistic and/or find the p-value.
4. State the conclusion that addresses the original claim.