For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5140 permanent dwellings on an entire reservation showed that 1683 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.) _______lower limit_______upper limit

Give a brief interpretation of the confidence interval.

A. 99% of all confidence intervals would include the true proportion of traditional hogans.

B. 99% of the confidence intervals created using this method would include the true proportion of traditional hogans.

C. 1% of the confidence intervals created using this method would include the true proportion of traditional hogans.

D. 1% of all confidence intervals would include the true proportion of traditional hogans.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

A. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal.

B. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial.

C. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial.

D. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal.