The starting salary of new graduates from State University in 2005 was $35,000. The distribution of salaries is known to be normal with a population standard deviation of $3,200. The University placement office suspects that salaries have changed. A random sample of 10 graduates was taken and their starting salaries are:

33,000

37,000

34,000

45,000

38,000

35,000

41,000

39,000

38,000

35,000

Is there enough evidence to support the University placement office's suspicion that the average starting salary has changed from $35,000 at the 1% significance level?

Show the steps of hypothesis testing using the P-value approach.

Be sure to interpret your result in the context of the problem.