A career counselor claims that the mean annual salary of athletic trainers in New Mexico and Arizona is the same. The mean annual salary of 40 randomly selected athletic trainers in New Mexico is $35,630. Assume the population standard deviation is $4800. The mean annual salary of 35 randomly selected athletic trainers in Arizona is $39,440. Assume the population standard deviation is $6200. At α = 0.10, is there enough evidence to reject the counselor’s claim?

(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.