A helmet manufacturer claims that the variance of the thickness in a helmet model is 7.5. A random sample of 15 helmets has a variance of 2.7. At α = 0.10, is there enough evidence to reject 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.