City A claims that the variance of its drunk-driving accidents is less than the variance of the drunk-driving accidents in City B. A sample of the drunk-driving cases of 15 of City A's accidents has a variance of 1.9. A sample of the drunk-driving cases of 20 of City B's accidents has a variance of 3.6. At \(\alpha=0.01\), can you support City A's claim?

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value and identify the rejection region,

(c) find the test statistic \(F,\) 

(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.