For this problem, carry at least four digits after the decimal in your calculati

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 5140 permanent dwellings on an entire reservation showed that 1578 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. (b) Find a 99% confidence interval for p. 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. 1% of all confidants 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 beta is approximately normal. Yes, the conditions are satisfied. This is important because if allows us to say that beta is approximately binomial. yes, the conditions are satisfied. This is important because it allows us to say that beta is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that beta is approximately binomial.

Explanation / Answer

n = 5140 , X = 1578

a) p^ = X/n = 1578/5140 = 0.307003

= 0.3070

b) 99 % confidence interval is

(p^ - z *sqrt(p^q^/n) , ((p^ - z *sqrt(p^q^/n) )

z =2.576 for 99 % CI

sqrt(pq/n) = sqrt(0.3070*0.693/5140)=0.0064336

z *sqrt(p^q^/n) = 2.576 *0.0064336 =0.016572

hence

lower limit = 0.3070 - 0.016572 =0.290428

upper limit = 0.3070 + 0.016572 =0.323572

option A) si correct

99 % of confidence intervla created using this method include the true proportion

c) np = X = 1578 > 5

nq =n-X = 5140-1578 > 5

yes , the conditions are satisfied , this si impotant because it allows us to sya that p^ is approximately normal

option C) ic correct

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