Q.96
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct) +4 −1
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:

Stratum $i$$N_i$Pop. $M_i$Pop. $MS_i$ ($S_i^2$)
13002525
22005100
Then the sample sizes using proportional and Neyman allocations are given by:
Q.97
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct) +4 −1
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:

Island $i$Size of island $i$ (sq miles)Palm trees $y_i$
1110
29550
36225
29550
Then the Horvitz-Thompson estimate for estimating the total number of trees is:
Q.98
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct) +4 −1

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
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct) +4 −1
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
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct) +4 −1
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,

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