MST-013 IGNOU Solved Assignment 2026-27

MST-013 Solved Assignment: Survey Sampling and Design of Experiments-I (TMA Solutions)

This verified digital PDF guide aligns with IGNOU’s M.Sc. (Applied Statistics) curriculum, offering 30% course weightage solutions for MST-013 TMAs. It includes step-by-step derivations, real-world applications, and adherence to academic session deadlines. Below are the key syllabus blocks with solved examples:

1. Block-1: Simple Random Sampling and Probability Proportional to Size Sampling

• Simple Random Sampling (SRS): Definition, advantages, and bias mitigation techniques with solved problems on sampling frame construction.
• Probability Proportional to Size (PPS) Sampling: Step-by-step derivation of PPS with replacement/without replacement, including variance estimation for finite populations.
• Practical Example: Application in agricultural yield surveys (e.g., estimating wheat production in a district) with 500-word solution.

2. Block-2: Stratified and Systematic Samplings

• Stratified Sampling: Optimal allocation methods (Neyman, proportional) with solved case studies on human blood group distribution in a city.
• Systematic Sampling: Interval calculation, efficiency comparison with SRS, and error analysis in industrial quality control.
• Key Formula: Variance reduction in stratified sampling: V_strat = Σ(N_h/N (1 − n_h/N_h) S_h²) with solved numerical.

3. Block-3: Analysis of Variance (ANOVA)

• One-Way ANOVA: Partitioning variance (between-group vs. within-group), F-test derivation, and assumptions (normality, homogeneity of variance).
• Post-Hoc Tests: Tukey’s HSD with solved example comparing fertilizer effects on plant growth (3 treatments, 5 replications).
• Real-World Link: ANOVA in clinical trials (e.g., drug efficacy testing) with 250-word solution.

4. Block-4: Design of Experiments (DOE)

• Completely Randomized Design (CRD): Layout, error terms, and power calculation for agricultural experiments.
• Randomized Block Design (RBD): Blocking variables (e.g., soil type), solved example for crop yield comparison.
• Latin Square Design: Application in chemical experiments (e.g., drug interaction studies) with 100-word concise solution.

Subject-Specific FAQs

• Q: How do I calculate sample size for PPS sampling?

  A: Use the formula n = N / (1 + N (C² σ² / (N * S²))), where C is the coefficient of variation of sizes. Example: For a population of 1000 farms with σ=15 and S=50, solve for n.

• Q: When should I use stratified vs. systematic sampling?

  Stratified sampling is ideal for heterogeneous populations (e.g., urban vs. rural households), while systematic sampling is efficient for ordered lists (e.g., production lines). Choose based on variance reduction needs and sampling frame accessibility.

Note: All solutions comply with IGNOU’s current academic session guidelines (e.g., 500 words for Block-1, 250 words for Block-3) and include step-by-step derivations for full marks.