Navajo Culture: Traditional Hogans S. C. Jett is a professor of geography at the University of California, Davis. He and a colleague, V. E. Spencer, are experts on modern Navajo culture and geography. The following information is taken from their book Navajo Architecture: Forms, History, Distributions (University of Arizona Press). On the Navajo Reservation, a random sample of 210 permanent dwellings in the Fort Defi ance region showed that 65 were traditional Navajo hogans. In the Indian Wells region, a random sample of 152 permanent dwellings showed that 18 were traditional hogans. Let p1 be the population proportion of all traditional hogans in the Fort Defi ance region, and let p2 be the population proportion of all traditional hogans in the Indian Wells region.

(a) Find a 99% confi dence interval for p1  p2.

(b) Interpretation Examine the confi dence interval and comment on its meaning.

Does it include numbers that are all positive? all negative? mixed?

What if it is hypothesized that Navajo who follow the traditional culture of their people tend to occupy hogans? Comment on the confi dence interval for p1  p2 in this context.