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 0.2, while a sample of the fuel consumptions of 21 of its competitor's hybrids has a variance of 0.45. At a = 0.01, can you support the manufacturer's claim? Fill in the following blanks.
Ho: The variance of the fuel consumptions for the manufacturer's hybrids is greater than or equal to the variance of the fuel consumptions for the competitor's hybrids.
HA: The variance of the fuel consumptions for the manufacturer's hybrids is less than the variance of the fuel consumptions for the competitor's hybrids.
dfn = 19 - 1 = 18
dfd = 21 - 1 = 20
Critical value = F(0.01, 18, 20) = 0.432
Test statistic F = (0.2/0.45) * (21 - 1)/(19 - 1) = 0.888
Decide whether to reject or fail to reject the null hypothesis: Since the test statistic F (0.888) is greater than the critical value (0.432), we fail to reject the null hypothesis. Therefore, we do not have enough evidence to support the manufacturer's claim that the variance of the fuel consumptions for its hybrid vehicles is less than the variance of the fuel consumptions for the competitor's hybrids.