AP Statistics · Unit 8 · Inference for Categorical Data: Chi-Square

Library staff selected a random sample of 400 checkout records from the past year and classified each record by the patron's age group (under 25, or 25 and older) and the format checked out (print, e-book, or audiobook). The results are shown in the two-way table below.

Staff want to know whether age group and format are associated among all patrons of the library.

(a) Assuming age group and format are independent, what is the expected count of patrons 25 and older who checked out e-books? Compare it with the observed count of 60, and explain what the comparison suggests.
(b) What is this cell's contribution to the chi-square test statistic? Explain what a relatively large contribution from one cell tells the library staff.
(c) The other expected counts, rounded to the nearest tenth, are shown below.

Do these data provide convincing statistical evidence, at $\alpha = 0.05$, of an association between age group and format checked out among all patrons of the library? Carry out an appropriate test, using the critical value $\chi^2 = 5.991$ ($df = 2$).
(d) The library director claims that the cell you examined in parts (a) and (b) — patrons 25 and older checking out e-books — accounts for the majority of the overall chi-square statistic from part (c). Does the contribution you calculated in part (b), compared to the overall test statistic from part (c), support the director's claim? Justify your answer.