On the Navajo Reservation, suppose that a random sample of 222 permanent dwellings in the Fort Defiance region showed that 62 were traditional Navajo hogans. Suppose
that in the Indian Wells region, a random sample of 153 permanent dwellings showed that 18 were traditional hogans. Let $p_1$ be the population proportion of all traditional
hogans in the Fort Defiance region, and let $p_2$ be the population proportion of all traditional hogans in the Indian Wells region.
USE SALT
(a) Can a normal distribution be used to approximate the $p_1 - p_2$ distribution? Explain.
The data constitute two independent samples. Calculating the following quantities $np_1 = \text{________}$, $n_1(1 - p_1) = \text{________}$, $n_2p_2 = \text{________}$, and
$n_2(1 - p_2) = \text{________}$, we see that all these quantities are greater than 5. So, the normal distribution can be used to approximate the $p_1 - p_2$
distribution.
(b) Find a 99% confidence interval for $p_1 - p_2$. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to three
decimal places.)
