MST-020 IGNOU Solved Assignment 2026-27

MST-020 Solved Assignment: Survey Sampling and Design of Experiments-II

This verified TMA solution set for MST-020 (English/Hindi) strictly follows the official IGNOU curriculum for the M.Sc. (Applied Statistics) program, School of Sciences (SOS). Each block is addressed with precise mathematical derivations, real-world applications in natural/physical sciences, and adherence to word limits. Below are the key syllabus blocks covered:

Block 1: Use of Auxiliary Information in Estimation

Key topics include:

• Ratio and Regression Estimation: Mathematical formulation of ratio estimators (e.g., ŷ = r̄ * N/n) and regression estimators, with applications in agricultural yield surveys.
• Auxiliary Variables: Selection criteria (e.g., correlation, bias reduction) and bias/variance trade-offs in stratified sampling.
• Solved Example: Estimate population mean income using auxiliary data (e.g., education level) with 500-word limit compliance.

Block 2: Cluster and Two-Stage Samplings

Key topics include:

• Cluster Sampling Designs: Single-stage vs. two-stage sampling, with variance formulas for primary and secondary units (e.g., V(ŷ) = (1 f)² (N/n) (1 + (n-1)/N) * σ²).
• Applications in Ecology: Sampling forest plots or marine biodiversity using nested clusters.
• Solved Example: Calculate sample size for two-stage sampling in a botanical survey (250-word limit).

Block 3: Factorial Experiments

Key topics include:

• Design Principles: Orthogonal arrays, confounding, and resolution in 2^k and 3^k designs (e.g., Taguchi methods for physical sciences).
• Analysis of Variance (ANOVA): Partitioning sums of squares for factorial treatments (e.g., SS_Total = SS_FactorA + SS_FactorB + SS_Interaction).
• Solved Example: Interpret factorial data on catalyst efficiency in chemistry (100-word limit).

Block 4: Incomplete Block Designs

Key topics include:

• Latin Squares and Balanced Incomplete Block Designs (BIBD): Parameters (v, b, r, k, λ) and construction methods.
• Applications in Agronomy: Field experiments with unequal plot sizes or missing data.
• Solved Example: Design a BIBD for 9 treatments with 3 replicates (250-word limit).

FAQs for MST-020 TMA

• Q: How are auxiliary variables selected in ratio estimation?

  A: Auxiliary variables (e.g., soil pH for crop yield) are chosen based on high correlation (r > 0.7) with the study variable and minimal measurement error. IGNOU’s solutions prioritize variables like X (covariate) and Y (target) with E(X) = μ_X.

• Q: What is the difference between single-stage and two-stage cluster sampling?

  A: Single-stage samples entire clusters (e.g., villages) directly, while two-stage samples clusters first (e.g., villages) and then sub-units (e.g., households). Two-stage reduces cost but increases variance; formulas for V(ŷ) account for both stages.

Note: All solutions include step-by-step derivations, IGNOU-verified references (e.g., Srivastava & Chaturvedi), and submission-ready PDFs with deadlines (e.g., June/December session TMA deadlines).