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

A random sample of5100permanent dwellings on an entire reservation showed that1613were traditional hogans.

(a) Find a 99% confidence interval forp. (Round your answers to three decimal places.)

• lower limit =
• upper limit =

(b) Give a brief interpretation of the confidence interval.

• 1. 1% of the confidence intervals created using this method would include the true proportion of traditional hogans.
• 2. 1% of all confidence intervals would include the true proportion of traditional hogans.
• 3. 99% of the confidence intervals created using this method would include the true proportion of traditional hogans.
• 4. 99% of all confidence intervals would include the true proportion of traditional hogans.

(c) Do you think thatnp>5 andnq>5 are satisfied for this problem? Explain why this would be an important consideration.

• 1. No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.
• 2. Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.
• 3. No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.
• 4. Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.