Statistics Paper-III 2023 (ISS/IES) — OCR Repair
- Year 2023
- Conducted By ASRT-T-STT
- Questions 8
- Maximum Marks 200
- Duration Three Hours Maximum Marks: 200
- Languages English
Exam Details
| Detail | Information |
|---|---|
| Examination | Statistics Paper-III |
| Year | 2023 |
| Conducting Body | ASRT-T-STT |
| Paper | Statistics |
| Subject | Statistics |
| Duration | Three Hours Maximum Marks: 200 |
| Maximum Marks | 200 |
| Number of Questions | 8 |
| Question Type | Section-a descriptive; section-b descriptive |
This JSON contains the OCR-repaired content for Statistics Paper-III (2023) from the ISS/IES examination. It includes the exam metadata, a repaired objective questions preview with two descriptive questions (each with subparts), and a set of SEO-friendly fields for page optimization. Page 1 contributes the exam header, instructions, and exam mechanics, while Page 2 provides the repaired descriptive questions including price index calculation (Laspeyres, Paasche, Marshall-Edgeworth, Fisher), and advanced topics in regression variance (OLSE vs GLSE) and Neyman allocation in stratified sampling. The FAQ section consolidates key exam details for SEO relevance.
Major Topics Covered
- price index numbers
- Laspeyres index
- Paasche index
- Marshall-Edgeworth index
- Fisher's ideal index
- base year vs current year data
- linear regression
- OLS/GLS estimation
- variance of estimators
- efficiency comparisons
- correlation in GLS
- known vs unknown error variances
- weighted least squares
- Neyman allocation
- stratified sampling
- fpc (finite population correction)
- sampling variance
- administrative considerations in sampling
- data repair in OCR
- exam metadata extraction
Why This Paper is Important
- Useful for Statistics Paper-III preparation
- Helps understand the latest exam pattern
- Useful for practice and self-assessment
- Covers frequently asked General Studies topics
- Helpful for analysing question trends
Related Resources
Instructions
- There are EIGHT questions divided in TWO Sections.
- Candidate has to attempt FIVE questions in all.
Questions (page 2)
Q1. 1.
Q2.
(a) 2. Consider a simple linear regression model yi = β0 + β1 xi + ε_i, E(ε_i) = 0, V(ε_i) = σ_i^2, i = 1, 2, ..., n. Obtain the variance of ordinary least squares estimate (OLSE) and generalized least squares estimate (GLSE). Show that var(GLSE) ≤ var(OLSE). Also, show that the efficiency of OLSE and GLSE depends on the correlation between σ_i(xi - x̄) and (xi - x̄)/σ_i.
(b)
Discuss briefly the estimation procedure in the two cases when—
(i) σ_i^2, i = 1, ..., n are known;
(ii) σ_i^2, i = 1, ..., n are partially unknown (viz., σ_i^2 ∝ σ^2 Xi^{2λ}). With two strata, a sampler would like to have n1 = n2 for administrative
(c)
convenience, instead of using values given by Neyman allocation. If V(ȳ_st) and V_N(ȳ_st) denote the variances given by n1 = n2 and Neyman allocation respectively ignoring fpc, show that the fractional increase in variance
(V(ȳ_st) - V_N(ȳ_st)) / V_N(ȳ_st) = ((r-1)/(r+1))^2 α
Question paper preview
Scanned pages 1–2 for reference. Download the official PDF for the full paper.
Free question paper download
Download question paper PDF
Your download starts in 10s
Preparing your question paper file…
Frequently asked questions
What is the duration of Statistics Paper-III?
Three hours.
What is the maximum marks for the paper?
200 marks.
How many questions must a candidate attempt?
Eight questions are in the paper; candidates must attempt five in total.
Which section questions are compulsory?
Both questions in Section-A are compulsory.
In which language must answers be written?
Answers must be written in English only.
What is the conducting body or code for this paper?
ASRT-T-STT (Statistics Paper-III).