A company is experimenting with synthetic fibers as a substitute for natural fibers. The quality characteristic of interest is the breaking strength. A random sample of 8 natural fibers yields an average breaking strength of 540 kg with a standard deviation of 55 kg. A random sample of 10 synthetic fibers gives a mean breaking strength of 610 kg with a standard deviation of 22 kg.
(a) Can you conclude that the variances of the breaking strengths of natural and synthetic fibers are different? Use a level of significance α of 0.05. What assumptions are necessary to perform this test?
(b) Based on the conclusions in part (a), test to determine if the mean breaking strength for synthetic fibers exceeds that for natural fibers. Use a significance level α of 0.10.
(c) Find a two-sided 95% confidence interval for the ratio of the variances of the breaking strengths of natural and synthetic fibers.
(d) Find a two-sided 90% confidence interval for the difference in the mean breaking strength for synthetic and natural fibers.