In Kenya, human induced land-use changes and excessive resource extraction have threatened the jungle ecosystem by reducing animal grazing areas and disrupting access to water sources. In Landscape & Ecology Engineering (Jan. 2013), researchers compared hippopotamus grazing patterns in two Kenyan areas: a national reserve and a community pastoral ranch. Each area was subdivided into plots of land. The plots were sampled (406 plots in the national reserve and 230 plots in the pastoral ranch), and the number of hippo trails from a water source was determined for each plot. Sample statistics are provided in the table. Suppose the researchers want to know if the variability in number of hippo trails from a water source in the National Reserve differs from the variability in number of hippo trails from a water source in the pastoral ranch.

a. Find an interval estimate of σ21/ σ22, the ratio of the variances associated with the two areas. Use a 90% confidence level.
b. Can the researchers reliably conclude that the variability in number of hippo trails from a water source in the National Reserve differs from the variability in number of hippo trails from a water source in the pastoral ranch? Explain.
c. Explain why a test of hypothesis at α = .10 will result in the same inference, then carry out the test to verify your results.

National Reserve Pastoral Ranch Sample size Mean number of trails Standard deviation 406 .31 .40 230 .13 .30