Use R markdown to answer Questions 3 and 4. For these questions, the R output will not be sufficient. Give a sentence or two to answer the question.

3) Consider the data in the countiesA.csv file. The file contains a few variables calculated from an (simple random sample) of 100 US counties out of N = 3141 counted. The variable PHYSICIA is the number

number of doctors in the county and the TOTPOP variable is the number of residents in the county. Use the survey library for the estimates below. During the period of this survey, the total number of inhabitants in the US was 255,077,536.

(a) Estimate the total number of physicians in the US and give the estimated standard error.

(b) Estimate the total number of doctors by a quotient using the number of inhabitants as a variable

auxiliary and give the estimated standard error.

(c) Estimate the total number of physicians by regression using the number of inhabitants as

auxiliary variable.

(d) The true total number of physicians was 532,638. Which of the estimates is closest to the true?

value.

4. Refer to the data from Question 4. Assuming the name of the dataset is counties,

consider the following command:

counties $ x <-as.numeric (counties $ TOTPOP <100000)

The command will add an indicator variable x to the dataset. The variable is xi = 1, if county i

has a population of less than 100,000, otherwise xi = 0.

(a) Using the svyratio function, estimate the average number of doctors per county in the field of

counted with a population of less than 100,000 inhabitants. Hint: define u = x y.

(b) Using the svytotal function, estimate the total number of physicians in the area of counties with

a population of less than 100,000 inhabitants. Hint: define u = x y.