An automobile manufacturer claims that the variance of the fuel consumptions for its hybrid vehicles is less than the variance of the fuel consumptions for the hybrid vehicles of a top competitor. A sample of the fuel consumptions of 19 of the manufacturer’s hybrids has a variance of 0.21. A sample of the fuel consumptions of 21 of its competitor’s hybrids has a variance of 0.45. At α = 0.01, can you support the manufacturer’s claim?

(a) Identify the claim and state H₀ 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. If convenient, use technology.