A guidance counselor claims that high school students in a college preparation program have higher ACT scores than those in a general program. The mean ACT score for 49 high school students who are in a college preparation program is 22.2. Assume the population standard deviation is 4.8. The mean ACT score for 44 high school students who are in a general program is 20.0. Assume the population standard deviation is 5.4. At α = 0.10, can you support the guidance counselors 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.