An education researcher claims that the mean high school graduation rate per state in the United States is 80%. You want to test this claim. You find that a random sample of 30 states has a mean high school graduation rate of 82%. Assume the population standard deviation is 5.1%. At α = 0.05, do you have enough evidence to support the researcher’s claim?

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

(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.