To compare the braking distances for two types of tires, a safety engineer conducts 35 braking tests for each type. The mean braking distance for Type A is 42 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Type B is 45 feet. Assume the population standard deviation is 4.3 feet. At α = 0.10, can the engineer support the claim that the mean braking distances are different for the two types of tires?

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

(b) Find the critical value(s) and identify the rejection region(s),

(c) Find the standardized test statistic z,

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

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.