| Stratum $i$ | $N_i$ | Pop. $M_i$ | Pop. $MS_i$ ($S_i^2$) |
|---|---|---|---|
| 1 | 300 | 25 | 25 |
| 2 | 200 | 5 | 100 |
Q.96
A sample of 100 employees is to be drawn from a population divided into two strata. The strata population sizes $N_i$, population means (Pop. $M_i$) and the population mean squares (Pop. $MS_i$) of their monthly wages are given below:
Then the sample sizes using proportional and Neyman allocations are given by:
Q.97
Consider the problem of estimating the total number of palm trees on 100 islands in a tropical paradise. The area of each island is known and it is reasonable to think that the number $y_i$ of palm trees on each island is approximately proportional to the size of the island. The total size of these 100 islands is 100 square miles. Let the units selected with replacement in 4 independent draws be the islands numbered 1, 29, 36 and 29 with information details as follows:
Then the Horvitz-Thompson estimate for estimating the total number of trees is:
| Island $i$ | Size of island $i$ (sq miles) | Palm trees $y_i$ |
|---|---|---|
| 1 | 1 | 10 |
| 29 | 5 | 50 |
| 36 | 2 | 25 |
| 29 | 5 | 50 |
Q.98
Consider the following statements to estimate the total marine fish landings of our country:
(A) . Even though the sampling design adopted for the purpose is ‘stratified multistage random sampling’ and stratification
being done over space and time, cluster sampling and double sampling are also involved for selecting first stage units.
(B) . A month is divided into 3 groups of 10 consecutive days. Suppose that the 4th date (day) was selected from the group of
first 10 days of a month. Then 6 consecutive days from the selected day will be 4, 5, 6, 7, 8, 9 and these days are grouped
into 3 clusters of 2 consecutive days, i.e., dates (4 and 5) will form one cluster, while (6 and 7) and (8 and 9) will form the
other two clusters. From the 2nd group of 10 days, 6 days are systematically selected with a sampling interval of 10 days
from the first date selected from the group of first ten days. Thus 6 days In the 2nd group will be 14, 15, 16, 17, 18 and 19
forming 3 clusters of dates (14 and 15), (16 and 17) and (18 and 19). From the 3rd group. 6 days are selected with the
sampling interval of 10 days from the first day selected in the 2nd group, ie., the dates will be 24, 25, 26, 27, 28 and 29
whose clusters are (24 and 25), (26 and 27), (28 and 29). Thus there are 9 clusters of two days each in a month
(C) . Each maritime state is divided into several zones on the basis of geographical consideration and fishing practices. Nine
landing centres are selected at random from each zone for recording fish landings. Then 9 clusters, formed by a certain
procedure involving systematic sampling also within a month, are allotted randomly to the 9 selected landing centres
(D) . On the first day of observation data are collected from 6 AM to 12 Noon and in the next day, 12 Noon to 6 PM. The data
on night landings are collected by enquiry covering the period from 6 PM of the first day to 6 AM of the next day. Thus a 24
hour period is covered for a landing centre. This forms the ‘landing centre day’ and is the first stage sampling unit.
Choose the correct statements from the options given below:
Q.99
Consider the population U = {1, 2, 3} with P({1, 2}) = 1/2; P((1, 3}) = 1/4;
P({2, 3}) = 1/4. Then if 1% denotes the first order inclusion probability of the k-th unit (k=1, 2, 3),
which of the following is NOT
true’
Q.100
Avillage has 10 orchards numbered 1 to 10 containing 150, 50, 80, 100, 200, 160, 40, 220, 60, 140 trees respectively. It is
desired to select a sample of 4 orchards PPS With Replacement to the number of trees in the orchard. By cumulative total
method, if the random numbers chosen in the successive draws are 600, 650, 850 and 300,
Design of Experiments
4 टॉपिक्स
Linear Estimation, Gauss-Markov Theorem & Basic Experimental Designs (CRD, RCBD, Latin Square Design)
Factorial Experiments (2^n, 3^n Series), Complete & Partial Confounding Mechanics
Incomplete Block Designs: Balanced Incomplete Block Designs (BIBD), PBIBD & Lattice Designs
Split-Plot, Strip-Plot, Crossover Designs & Analysis of Covariance (ANCOVA)
खंड अ: सामान्य कृषि
5 टॉपिक्सSample Surveys
3 टॉपिक्सStatistical Genetics
3 टॉपिक्स
Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients
Quantitative Genetics: Variance Partitioning, Heritability, Repeatability, Path Analysis & Selection Indices
Mendelian Genetics, Linkage Estimation, Recombination Frequencies & Three-Point Test Cross Mapping
Statistical Methods I
3 टॉपिक्सStatistical Methods II
3 टॉपिक्स
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization
Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests
Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis
Official PYQ Papers
Previous Year Papers of Agricultural Statistics
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2024
29-06-2024