ADVANCED TECHNIQUES OF SAMPLE SURVEYS — DU B.Sc (hons) Statistics Previous Year Question Papers

Attempt six questions in all. (b) Show that the estimator Î of the population total T obtained under a balanced sampling scheme, which is BLUE under the model Y; = Bx; + ei[x;]/2 ; i = 1,2,...,N. remains BLUE under the extended model Y; = a + Bx; + E¡[x;]1/2 ', i = 1,2,...,N. (5.10) (b) Suppose that n first-stage units are selected by simple random sampling without replacement (SRSWOR), and from each selected first-stage unit, m second-stage units are further selected using SRSWOR. Show that the sample mean y is an unbiased estimator of the population mean Y. Also, show that its sampling variance is given by N n M nm where notations have their usual meanings. (5,10) 6. A population consists of N clusters each containing M elements. A simple random sample of n clusters is selected to estimate the population mean per element. Assume that Su, the variance within clusters, is given by aM", b > 0 and the cost function is C = GnM + C.Vn. Find the optimum size of the cluster that minimizes the variance of the estimator given that the cost of survey is fixed. (15) 7. In a survey, the expected response rate is 1/3 and S} = S2. It costs Rs 1.00 to include a unit in the sample, Rs 5.00 of getting information per unit in the response class, and Rs 9.00 of collecting information per unit in the non-response class. Obtain (a) the optimal values of k and n so that the mean value of the population is estimated with (b) If the overhead cost is Rs 267, determine the expected cost of the survey. (7,8) 8. Write a short note on the following. (a) Hansen and Hurwitz. - Call-back methods. (b) Types of non-response. (c) Circular systematic sampling. (5, 5, 5)