The contingency table shows a random sample of urban, suburban, and rural libraries by the speed of their Internet access. In the table, mbps represents megabits per second. At α = 0.01, can you conclude that the metropolitan status of libraries and Internet access speed are related?

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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Internet access speed 6.0 mbps or less 6.1 mbps-20.0 mbps Greater than 20.0 mbps Metropolitan status Urban Suburban Rural 67 36 23 46 51 91 20