On the Navajo Reservation, a random sample of 228 permanent dwellings in the Fort Defiance region showed that 54were traditional Navajo hogans. In the Indian Wells region, a random sample of 143 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. (Round your answer to three 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. Because the interval contains only negative numbers, we can say that there is a higher proportion of hogans in the Indian Wells region. We can not make any conclusions using this confidence interval.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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On the Navajo Reservation, a random sample of 228 permanent dwellings in the Fort Defiance region showed that 54were traditional Navajo hogans. In the Indian Wells region, a random sample of 143 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. (Round your answer to three 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.

Because the interval contains only negative numbers, we can say that there is a higher proportion of hogans in the Indian Wells region.

We can not make any conclusions using this confidence interval.

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