How much more do public colleges and universities charge out-of-state students for tuition per year? A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data for students entering as Freshmen in Fall 2013.

a) Create a 90% confidence interval for the mean difference in cost. Be sure to justify your procedure.
b) Interpret your interval in context.
c) A national magazine claims that public institutions charge state residents an average of $7000 less than out-of-stators for tuition each year. What does your confidence interval indicate about this assertion?

Institution Univ of Akron (OH) Athens State (AL) Ball State (IN) Bloomsburg U (PA) UC Irvine (CA Central State (OH) Clarion U (PA) Dakota State Fairmont State (WW) Johnson State (VT) Lock Haven U (PA) New College of Elorida Oakland U (MI) U Pittsburgh Savannah State (GA) Louisiana State W Liberty University (WV)6226 Central Texas College Worcester State (MA) Resident Nonresident 10,130 5,760 10.770 9,610 24,124 8,582 18,516 13,149 36,027 6,058 13,510 9,404 12716 8.286 10.286 5.824 12288 10.286 21,950 8,898 16,832 6,783 29,812 10,613 23,873 17,100 27,106 6,340 18,542 5,241 18,494 12,288 10.93 13.540 6,270 14,230 2,130 8,157