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 5,300 permanent dwellings on an entire reservation showed that 1,641 were traditional hogans. (a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find point estimates for p and q. (Round your answers to four decimal places.) A (b) Find a 99% confidence interval for p. Find the maximal margin of error, &. (Round your answer to three decimal places.) F - Report the bounds from the 90%% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit Give a brief interpretation of the confidence interval, O) 1% of all confidence intervals would include the true proportion of traditional hogans. 0 99% of the confidence intervals created using this method would include the true proportion of traditional hogans. O 99% of all confidence intervals would include the true proportion of traditional hogans. O 1% of the confidence intervals created using this method would include the true proportion of traditional hogans. (c) Do you think that op > 5 and no > 5 are satisfied for this problem? Explain why this would be an important consideration. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that f is approximately normal. O No, the conditions are not satisfied, This is important because it allows us to say that @ is approximately binomial