please use the sample I'm attaching a pic

this is the formula you can use Also N is 50 and population total is 288368698. please well explain both parts

8.1 The data set USPOP in Appendix C and on the data disk gives the percentage of people ages 65 and over for each state. Using these percentages from a random sample of ten states, estimate the percentage of people ages 65 and over in the United States as a whole for 2000, with a bound on the error of estimation, using a. a ratio estimator based on each state being a cluster of people. b. a simple average of the percentages for the sampled states. Compare the two techniques and comment on which one you prefer. % in poverty 15.2 7.8 65 and over 588542 472314 166910 355094 151141 11.4 State Total 1 Alabama 4486508 2 onnecticut 3460503 3 Hawai 1244898 4 Kanas 2715884 5 Idaho 1341131 6 Minnesota 5019720 7 Ohio 11421267 8 ode Island 1069725 9 st Verginia 1801873 10 Texas 21779893 10.1 11.4 6.9 601741 1513372 152286 275974 2152896 10.1 10.3 16.6 15.3 6430270 115.1 54341402 Total The following notation is used in this chapter. N=the number of clusters in the population n=the number of clusters selected in a simple random sample m = the number of elements in cluster i, i = 1,...,N m;= the average cluster size for the sample N M = m = the number of elements in the population M = M/N = the average cluster size for the population y,= the total of all observations in the ith cluster The estimator of the population mean u is the sample mean y, which is given by 1 11 Thus, y takes the form of a ratio estimator, as developed in Chapter 6, with m, taking the place ofx. Then the estimated variance of y has the form of the variance of a ratio estimator, given by Eq. (6.2). Ratio estimator of the population mean : TI Eyi i=1 (8.1) y 11 Estimated variance of y: um-( - ) (8.2) NnM where 20 - ym.) 2 (8.3) al Here M can be estimated by mif M is unknown