Harvard University has recently revolutionized its financial aid policies, aimed at easing the financial strain on middle and upper-middle income families (Newsweek, August 18-25, 2008). The expected contribution of students who are admitted to Harvard has been greatly reduced. Many other elite private colleges are following suit to compete for top students. The motivation for these policy changes stems from the competition from public universities as well as political pressure.
A spokesman from an elite college claims that elite colleges have been very responsive to financial hardships faced by families due to rising costs of education. Now, he says, families with income of $40,000 will have to spend less than $6,500 to send their children to prestigious colleges. Similarly, families with incomes of $80,000 and $120,000 will have to spend less than $20,000 and $35,000, respectively, for their children's education.
Although in general, the cost of attendance has gone down at each family-income level, it still varies by thousands of dollars amongst prestigious schools. The accompanying table shows information on the cost of attendance by family income for 10 prestigious schools. (The data can be accessed from the text website and are labeled Family Income.)
Family Income
School 40,000 80,000 120,000
Amherst College 5,302 19,731 37,559
Bowdoin College 5,502 19,931 37,758
Columbia University 4,500 12,800 36,845
Davidson College 5,702 20,131 37,958
Harvard University 3,700 8,000 16,000
Northwestern University 6,311 26,120 44,146
Pomona Colelge 5,516 19,655 37,283
Princeton University 3,887 11,055 17,792
Univ. of California system 10,306 19,828 25,039
Yale university 4,300 6,048 13,946
In a report, use the sample information to:
1.
Determine whether families with income of $40,000 will have to spend less than $6,500 to send their children to prestigious colleges. (Use α = 0.05.)
2.
Repeat the hypothesis test from part 1 by testing the spokesman's claims concerning college costs for families with incomes of $80,000 and $120,000, respectively. (Use α = 0.05.)
3.
Assess the validity of the spokesman's claims.