SURVEY SAMPLING AND DESIGN OF EXPERIMENTS — DU B.Sc (hons) Statistics Previous Year Question Papers

(b) How is the efficiency of a design is measured? Derive the expression to measure the efficiency of LSD over RBD, taking columns of LSD as blocks, stating clearly the assumption used in the derivation. (9,9) Do remaining four questions from Section A and B, selecting two questions from each section. 1. (a) Following is the incomplete ANOVA table for 3 treatments and total 24 observations Identify the design and complete the ANOVA table (b) An agricultural scientist wants to study the effect of four varieties of wheat V1, V2, V3, V4 on crop yield. A field is divided into 20 plots. The varieties are assigned to the plots at random, each variety being grown on five plots. Since soil fertility varies across the field, the field is divided into five blocks of equal size. Identify and explain the following : 1. Name and Number of treatments (b) Define (a) treatment contrast (b) orthogonal treatment contrast. be the linear combinations of treatment means. (i) Are X, Y, Z contrast? (ii) Which of these XY, YZ and ZX are orthogonal? (9,9) 7. (a) Explain Yates technique for calculating sum of squares due to main effects and interaction effects in case of 23 factorial experiment with r replications. Also write down the corresponding ANOVA table. (b) Obtain the layout of following designs 2. Name and Number of experimental units (i) A CRD with three treatments A, B and C, the replication number being 6, 5 and 3. Number of replications 4. The principles of design used in this experiment (ii) An RBD with 5 treatments in four blocks. 5. The design being used (iii) A 6 x 6 Latin Square Design. (9,9) (c) Calculate the minimum number of replications required so that an observed difference of 10% of the mean p will be regarded as significant at 5% level of significance, given that the coefficient of variation of plot value is 12%. 6. (a) Show that in a Latin Square Design, the mean sum of squares due to error is always an unbiased estimator of the error variance while mean sum of squares due to treatments is biased estimates of the error variance. Under what condition does it become unbiased for error variance? (d) Describe briefly the advantages of carrying out a sample survey in preference to a complete enumeration survey. Under what circumstances can complete enumeration be recommended in preference to a sample survey? (e) Describe the rule for determining the sample sizes to be allocated different strata if Neyman’s optimum allocation. (f) Define (a) Sampling unit, (b) Sampling frame, (c) Finite population correction factor, and (d) Non-sampling error. (3×6) 2. Define S.R.S. (i) with replacement, (ii) without replacement from a finite population. Derive the unbiased estimates of the population mean and its variance based on the above two methods. Compare the efficiencies of the estimates of the population mean. (18) 3. Explain the purpose of stratification in sample surveys.