A school administrator claims that the standard deviation for grade 12 students on a vocabulary assessment test is greater than 45 points. A random sample of 25 grade 12 test scores has a standard deviation of 46 points. At α = 0.01, is there enough evidence to support the 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 x², 

(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 population is normally distributed.