51. The standard deviation of the marks obtained in mathematics by 109 students is found to be 12. The standard error of the estimator of the population mean for a random sample of size 9 using SRSWOR is:
(a) 3.58
(b) 3.45
(c) 3.85
(d) 4.00
(a) 3.58
(b) 3.45
(c) 3.85
(d) 4.00
Answer: (c)
52. For stratified random sampling, consider the following statements:
1. Units within each strata are as heterogeneous as possible
2. The strata mean are as homogeneous as possible
1. Units within each strata are as heterogeneous as possible
2. The strata mean are as homogeneous as possible
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Answer: (d)
53. The theory of sampling is based on which of the following important principles?
1. Statistical regularity
2. Validity
3. Optimization
1. Statistical regularity
2. Validity
3. Optimization
Select the correct answer using the code given below:
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Answer: (d)
54. Consider the following sampling procedures:
1. PPS
2. SRSWR
3. SRSWOR
1. PPS
2. SRSWR
3. SRSWOR
In which of the above sampling procedures each member of the population gets a definite
probability of being included in the sample?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
probability of being included in the sample?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Answer: (d)
55. A population of size 800 is divided into 3 strata. Following information is obtained:
![](data:image/png;base64,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)
A stratified random sample of size 120 is to be drawn from the population. The sizes of the samples from the three strata under proportional allocation scheme are respectively:
(a) 30, 40, 50
(b) 30, 45, 45
(c) 20, 40, 60
(d) 50, 40, 30
(a) 30, 40, 50
(b) 30, 45, 45
(c) 20, 40, 60
(d) 50, 40, 30
Answer: (b)
56. A population of size 800 is divided into 3 strata. Following information is obtained:
![](data:image/png;base64,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)
A stratified random sample of size 120 is to be drawn from the population. The sizes of the samples from the three strata under Neyman’s optimum allocation scheme are respectively:
(a) 30, 45, 45
(b) 20, 40, 60
(c) 20, 50, 50
(d) 20, 45, 55
(a) 30, 45, 45
(b) 20, 40, 60
(c) 20, 50, 50
(d) 20, 45, 55
Answer: (b)
57. Efficiency of the sample survey technique is measured by the inverse of the:
(a) Population variance
(b) Sample variance
(c) Sampling variance of the estimator
(d) Sample mean
(a) Population variance
(b) Sample variance
(c) Sampling variance of the estimator
(d) Sample mean
Answer: (c)
58. Every unit of the population is enumerated in :
1. Sample survey
2. Census
3. Design of experiment
1. Sample survey
2. Census
3. Design of experiment
Which of the above is/are correct?
(a) 1 only
(b) 2 only
(c) 1 and 2 only
(d) 1, 2 and 3
(a) 1 only
(b) 2 only
(c) 1 and 2 only
(d) 1, 2 and 3
Answer: (b)
59. The following information is obtained for a population of size 100 divided into two strata and a stratified random sample of size 30 was selected.
For this data, consider the following statements:
1. The variance under equal allocation is more than that of proportional allocation
2. Stratified sampling with equal allocation is more precise than that of proportional allocation
Which of the statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Answer: (b)
60. A population of size 5000 is divided into three strata in the ratio 2 : 5 : 3 with standard errors 5, 8 and 20 respectively. A sample of 150 units is to be selected from the population. Match List‐I(Sample units from strata 1, 2 and 3 respectively) with List‐II (methods of allocation) and select the correct answer using the code given below the lists:
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)
Code:
(a) A/2, B/3, C/1
(b) A/1, B/2, C/3
(c) A/2, B/1, C/3
(d) A/1, B/3, C/2
(a) A/2, B/3, C/1
(b) A/1, B/2, C/3
(c) A/2, B/1, C/3
(d) A/1, B/3, C/2
Answer: (No correct answer)
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