Question

On the Navajo Reservation, a random sample of 218 permanent dwellings in the Fort Defiance region showed that 60 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 19 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 95% 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

To calculate a 95% confidence interval for p1 - p2, find the point estimate and the error bound. The interval is (0.202, 0.349), indicating a higher proportion of hogans in the Fort Defiance region.

Step-by-step explanation:

To calculate a 95% confidence interval for p1 - p2, we first need to find the point estimate and the error bound.

The point estimate for p1 - p2 is (60/218) - (19/139) = 0.2757.

The error bound can be calculated using the formula: sqrt((p1 * (1 - p1)/n1) + (p2 * (1 - p2)/n2)). In this case, n1 = 218, n2 = 139, p1 = 60/218, and p2 = 19/139. Plugging in these values, we get an error bound of 0.0737.

Therefore, the 95% confidence interval for p1 - p2 is 0.2757 ± 0.0737, or (0.202, 0.349).

In this context, the confidence interval includes numbers that are all positive, indicating that there is a higher proportion of traditional hogans in the Fort Defiance region compared to the Indian Wells region.

Answer 2

Step-by-step explanation:

On the Navajo Reservation, a random sample of 218 permanent dwellings in the Fort Defiance region showed that 60 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 19 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 95% 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.