Question

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 5400 permanent dwellings on an entire reservation showed that 1620 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. 99% of the confidence intervals created using this method would include the true proportion of traditional hogans. 1% of the confidence intervals created using this method would include the true proportion of traditional hogans. 99% of all confidence intervals would include the true proportion of traditional hogans. 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. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

Answer 1

%Let x be the number of traditional hogans and n be the randomly selected sample of permanent dwellings on an entire reservation.

We are given x = 1620 and n = 5400

a) Point estimate of = x/n = 1620 / 5400 = 0.3000

We are asked to find 99% confidence interval for proportion .

We can use TI-84 calculator to find the CI for P

Press STAT ---> Scroll to TESTS ---> scroll Down to 1-Prop z "interval" and hit enter.

Then plug the given values accordingly,

Scroll to calculate and hit enter.

Lower limit = 0.284 , upper limit = 0.316

Interpretation :

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

c) here n = 5400 and P = 0.5 and q = 1 - 0.5 = 0.5

So nP = 2700 and nq = 2700 , so both nP and nq are greater than 5

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