A financial aid officer is studying the relationship between who borrows money for college in a family and the income of the family. As part of the study, 1611 families are randomly selected and the resulting data are organized as shown in the contingency table. At α = 0.01, can you conclude that who borrows money for college in a family is related to the income of the family?

Perform the indicated chi-square independence test by doing the following.

(a) Identify the claim and state H₀ and H_a.

(b) Determine the degrees of freedom, find the critical value, and identify the rejection region.

(c) Find the chi-square test statistic. If convenient, use technology.

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

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Who borrowed money Family income Less than $35,000 $35,000-$100,000 Greater than $100,000 Student only Parent only Both No one 168 255 62 40 85 38 20 266 46 386 17 228