The data below represent the tuition fees of a 4th year public college students. The colleges' boards claim that the average tuition fees per college is not exceeding $5836 per year. The fees in 15 public colleges were gathered as shown in table below. College Central Washington University University of Washington Washington State University Western Washington University Evergreen State University Eastern Washington University Peninsula University University of Oregon Portland State University Oregon State University Southern Oregon University Eastern Oregon University Western Oregon University University of Idaho Idaho State University Tuition Number of Students 10,200 25,469 18,432 13,000 4,400 10,000 10,120 20,394 24,284 19,362 5,000 3,000 4,500 11,739 13,000 $4392 $5985 $5888 $4356 $4590 $5904 $3639 $6174 $5208 $5604 $5233 $4500 $5763 $4410 $4400 Analyze the data, and verify if the board's claim, indeed, is true and if the cost of tuition is dependent on the number of students that attend. If you wish, you may use any computer software to analyze the data. A good analysis, as you might know, includes both graphical and analytical methods. Make any assumptions that are necessary. Verify your assumptions if necessary. Also, construct a 99% confidence interval on the true tuition fees mean. Good Luck