Question

On the Navajo Reservation, a random sample of 228 permanent dwellings in the Fort Defiance region showed that 56 were traditional Navajo hogans. In the Indian Wells region, a random sample of 145 permanent dwellings showed that 18 were traditional hogans. Let p₁ be the population proportion of all traditional hogans in the Fort Defiance region, and let p₂ be the population proportion of all traditional hogans in the Indian Wells region.

(a) Find a 90% confidence interval for p₁ – p₂. (Use 3 decimal places.)

lower limit
upper limit

(b) Examine the confidence 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 confidence interval for p₁ – p₂ in this context.

Because the interval contains only positive numbers, we can say that there is a higher proportion of hogans in the Fort Defiance region.

Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of hogans in the Fort Defiance region.     

We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of hogans in the Indian Wells region.

Answer 1