The mean ACT mathematics score for 60 high school students is 20.6. Assume the population standard deviation is 5.4. The mean ACT science score for 75 high school students is 20.8. Assume the population standard deviation is 5.6. At α = 0.01, can you reject the claim that ACT mathematics and science scores are equal?

(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, and 

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