The data file counties.dat contains information on land area, population, number of physicians, unemployment, and a number of other quantities for an SRS of 100 of the 3141 counties in the United States (U.S. Census Bureau, 1994). The total land area for the United States is 3,536,278 square miles; 1993 population was estimated to be
255,077,536.
a. Draw a histogram of the number of physicians for the 100 counties.
b. Estimate the total number of physicians in the United States, along with its standard error, using N.
c. Plot the number of physicians vs. population for each county. Which method do you think is more appropriate for these data: ratio estimation or regression estimation?
d. Using the method you chose in (c), use the auxiliary variable population to estimate the total number of physicians in the United States, along with the standard error.
e. The “true” value for total number of physicians in the population is 532,638. Which method of estimation came closer?