Question

PROBLEM 1 Suppose you wish to estimate the total number of physicians in the United States. County records of all counties contain the number of physicians in each county. The records furthermore contain information on the county size and the number of residents. A census also determined that in 1993 there were 255,077,536 residents in 3141 counties in the US. The total land area is 3,536,278 square miles. Suppose a random sample of 100 counties #of physicians in county i, Y population in county i. Suppose is obtained. Let X; = 118531, sy we calculate the following sample statistics: 297, sr 159, ỹ = 95687 and p = 0.68 Estimate the total number of physicians in the US using a ratio estimator (c) (d) Find the estimated standard error of the ratio estimate in part (c) Estimate the total number of physicians using the estimator tn from a simple random (e) sample and its standard error and compare it to the ratio estimator from (d). If you assume that the ratio estimator has a negligible bias, which estimator do you prefer?

Answer 1

Solution: Gven that the Sanple statistics メ= 393, 3x> 159, y-118531リ Sy:15684 and 0-68 9stimato Ratio 118531 297 399 09 staudard Srro the atio N-n 2stimated 9stinata whee, Se n-1 n-100, N- 3141 ) it CS Scanned with CamScanner 3

-) (n-1) Sn -) Se n-1 B Sy Syt B SySa2, sy 15693)(11.o151) 2(m o1) (0.68)4368(151) A 2BP S Sy t Estimated 3taudasd rro atio stimato Se 3141 -100 (2) 100 3141 1.098 x10 Aus 540 5 c.S Scanned with CamScanner