Question

Arvey af 2320 aduts in a cetain large cyged18 and older conducted by a reputabhe polthin oroniatn ound net 12 ve donatedblodin ne past twe years Conpee pares() trough belo (a) Obtain a point estimate for the population proportion of adults in the country aged 13 and older who have donated blood in the past two yea P 184 (Round to three decimal places as needed) (b) Verify that the requirements for constructing a confidence interval about p are satisfied The sample can be assumed to be a simple random sample, the value of np (1-D) 349 041 which is greater then ot equal to 10. and he i sample size can be assumed to be less then or equal to 5% of the population size. Round to three decimal places as needed c Construct and interpret a 0% confidence interval for the population proport on of adults in the county who have donated blood in he past two years Select the correct choice below and choice (Type integers or decimats rounded to three decimal places as needed Use ascending crder D who have donated blood in the past two yearsis between and I n any answer boxes within your A. We are % confident the proportion of adults in the country aged 18 and older OB. There is a 1% chance the proportion of adults in the country aged 18 and older who have donated b bioed n the pust iwo years is betweenand

Answer 1

$(a)~\hat{p}= 428/2320\approx 0.184\\ (b)~The~sample~can~be~assumed~to~be~a~simple~random~sample,~the~value~of~\\ n\hat{p}(1-\hat{p})=2320* 0.184*(1- 0.184)~is~348.334~which~is~greater~than~10~and~the~sample~\\ can~be~assumed~to~be~less~than~or~equal~to~5\%~of~the~population~size.\\ (c)~90\%~C.I.~of~p~is\\ \left(\hat{p}-Z_{0.05}\sqrt{\frac{\hat{p}(1-\hat{p})}{2320}} ,~\hat{p}+Z_{0.05}\sqrt{\frac{\hat{p}(1-\hat{p})}{2320}} \right )=(0.171,~0.198).\\ Option~A.~We~are~90\%~confident~the~proportion~of~adults~in~the~country~aged~18~and~older\\ who~have~donated~blood~in~the~past~two~years~is~between~0.171~and~0.198.$