You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved in passenger vehicle occupant deaths. As part of your study, you randomly select 4270 vehicle crashes and organize the resulting data as shown in the contingency table. At α = 0.05, can you conclude that the type of crash depends on the type of vehicle?

Perform the indicated chi-square independence test by performing the steps below.

(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.

(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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Vehicle Type of crash Single-vehicle Multiple-vehicle Car Pickup Sport utility 491 383 1059 507 1476 354