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 5000 permanent dwellings on an entire reservation showed that 1641 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.

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.

99% of the confidence intervals created using this method 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.

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

No, the conditions are not 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 normal.

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

Answer 1

The sampling distribuhon of a propornon follows as binomial distiputien and it is approximately normally distributed if np >5 and ng=n(-p)>5 We have used as z-value method here to calculate the confidence interval so it's important that the solistaibution is apportimately nomal as we are assuming that the popution is appooximately ncomal. Here of - 5000 * 0.3282 - 1641 >5 n = (-6) - Sooo * 2-6718 - 3351 25. : Answer is : Yes the conditions are satisfied. This is important because it allows us to say that p is appodrimately normal.