Construct a \(99 \%\) prediction interval for the average annual salary of postsecondary library science teachers when the average annual salary of librarians is \(\$ 56,000\). Interpret the results.

Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years. 

Librarians, .x Library science teachers, y 49.1 56.6 50.9 57.6 52.9 59.7 54.7 61.6 55.7 64.3 56.4 67.0 57.0 70.0 57.2 70.8 57.6 73.3 58.1 72.4 58.9 73.0 59.9 72.3