A random sample of the average debt (in dollars) at graduation from 30 of the top 100 public colleges and universities is listed below. Is there sufficient evidence at α = 0.01 to conclude that the population mean debt at graduation is less than $18,000? Assume σ = 2605.

Perform each of the following steps.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.

16,012 15,784 16,597 18,105 12,665 14,734 17,225 16,953 15,309 15,297 14,437 14,835 13,607 13,374 19,410 18,385 22,312 16,656 20,142 17,821 12,701 22,400 15,730 17,673 18,978 13,66 12,580 14,392 16,000 15,176