“The average college senior graduated this year with more than $19,000 in debt” was the beginning sentence of a recent article in USA Today. The majority of students have loans that are not due until the student leaves school. This can result in the student ignoring the size of debt that piles up. Federal loans obtained to finance college education are steadily mounting. The data given here show the amount of loans ($million)

for the last 13 academic years, with year 20 being the most recent.

Year Amount Year Amount Year Amount 1 9,914 8 16,221 15 37,228 2 10,182 9 22,557 16 39,101 3 12,493 10 26,011 17 42,761 4 13,195 11 28,737 18 49,360 5 13,414 12 31,906 19 57,463 6 13,890 13 33,930 20 62,614 7 15,232 14 34,376

a. Produce a time-series plot of these data. Indicate the time-series components that exist in the data.

b. Conduct a test of hypothesis to determine if there exists a linear trend in these data. Use a significance level of 0.10 and the p-value approach.

c. Provide a 90% prediction interval for the amount of federal loans for the 26th academic year.