EXAMPLE 6.8

Scholarship amount by borrower status. One purpose of Sallie Mae’s annual study described in Example 6.4 (page 350) is to allow comparisons of different subgroups. For example, in the latest report, 980 of the 1593 participants (61.5%) did not borrow any money to pay for college. The average scholarship amount among these participants was $3925. The average scholarship among those who did borrow was $4350. The difference of $425 is fairly large, but we know that these numbers are estimates of the population means. If we took different samples, we would get different estimates.

Can we conclude from these data that the average scholarship amounts in these two groups are different? One way to answer this question is to compute the probability of obtaining a difference as large or larger than the observed $425 assuming that, in fact, there is no difference in the population means. This probability is 0.23. Because this probability is not particularly small, we conclude that observing a difference of $425 is not very surprising when the population means are equal. The data do not provide enough evidence for us to conclude that the average scholarship amount for borrowers and non-borrowers differ.