A researcher wants to determine whether age is related to whether or not a tax credit would influence an adult to purchase a hybrid vehicle. A random sample of 1250 adults is selected and the results are classified as shown in the table. At α = 0.01, is there enough evidence to conclude that age is related to the response?

a. Identify the claim and state H₀ and H_a.

b. Use technology to enter the observed and expected frequencies into matrices.

c. Find the critical value X₀² and identify the rejection region.

d. Use technology to find the chi-square test statistic.

e. Decide whether to reject the null hypothesis. Use a graph if necessary.

f. Interpret the decision in the context of the original claim.

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Age Y es No Total Response 18-34 35-54 55 and older Total 189 261 450 257 218 475 143 182 325 589 661 1250