TGPSC MPSO / ASO · Paper II · Topic 7
TGPSC MPSO / ASO Sampling Techniques questions with answers
11 questions from TGPSC ASO Paper II Mock 1 with answers and TGPSC ASO Paper II Challenge 1 with answers. Try each one, then tap Show answer.
7.1Census vs sampling & sample sizeNotesPractise this chapter · Set 1 free
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No estimate of σ is available, but the values of a variable are known to range over about 120 units. Taking σ ≈ range/6, z = 2 and a margin of error of ±4, what sample size is needed?
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Answer B. 100
σ ≈ 120/6 = 20. n = (zσ/d)² = (2 × 20/4)² = 10² = 100.
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About 20% of the students in a district are believed to be anaemic. Using z = 2, how many students must be sampled to estimate this proportion within ±4 percentage points?
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Answer B. 400
n = z²pq/d² = 4 × 0.2 × 0.8/(0.04)² = 0.64/0.0016 = 400.
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An opinion poll uses a simple random sample of 625 voters. Taking p = 0.5 and z = 2, what is the margin of error of the sample proportion?
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Answer C. ±4 percentage points
SE = √(pq/n) = √(0.25/625) = 0.02. Margin = z × SE = 2 × 0.02 = 0.04, i.e. ±4 percentage points.
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Consider the following statements about sampling units:
1. Sampling units must not overlap, so that no unit of the population belongs to two of them.
2. Taken together, the sampling units must cover the whole population.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct. Sampling units must be clearly defined, non-overlapping and must together cover the whole population.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, sampling units; S.P. Gupta, Sampling)
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Consider the following statements:
1. A parameter, such as the population mean μ, is a fixed constant for a given population.
2. A statistic, such as the sample mean x̄, varies from one sample to another.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct. A parameter is a fixed population constant; a statistic is computed from a sample and varies from sample to sample.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, sampling units; S.P. Gupta, Sampling)
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A pilot survey suggests that about 20% of the 2,000 households in a mandal own a tractor. The proportion is to be estimated within ±0.04 with about 95% confidence (use z = 2). Using n0 = z²pq/d² and the finite population correction n = n0/(1 + n0/N), rounded up, what sample size is needed?
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Answer B. 334
About 334 households are needed. With p = 0.2 and q = 0.8, n0 = 4 × 0.16/0.0016 = 400. Correcting for N = 2,000, n = 400/(1 + 400/2000) = 400/1.2 ≈ 333.3, rounded up to 334.
Source: Standard method (BRAOU Sem5 Correlation, Regression & Sampling, sampling theory)
7.1Simple random samplingPractise this chapter · Set 1 free
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Which of the following hold for SRSWOR of size n (n > 1) from N units?
1. Every unit has probability n/N of being included.
2. The sample mean is unbiased for the population mean.
3. Var(ȳ) is smaller than under SRSWR of the same size.
4. The sample variance s² (divisor n − 1) is unbiased for σ² (divisor N).
Select the correct answer using the code given below.
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Answer D. 1, 2 and 3 only
1, 2 and 3 only. In SRSWOR, E(s²) = S² (divisor N − 1), not σ².
Source: Standard result (BRAOU Sem5 Unit 10; note: SRSWOR is the more precise design, Var(WOR) = (N − n)S²/(Nn) < Var(WR) = (N − 1)S²/(Nn))
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Consider the following:
Assertion (A): SRSWOR gives a more precise estimate of the population mean than SRSWR of the same size.
Reason (R): In SRSWOR no unit is repeated, so the sample contains more distinct units and more information.
Select the correct answer using the code given below.
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Answer A. Both A and R are true, and R is the correct explanation of A
Both are true and R explains A. Var(ȳ) WOR is smaller by the factor (N − n)/(N − 1).
Source: Standard result (BRAOU Sem5 Unit 10; note: SRSWOR is the more precise design, Var(WOR) = (N − n)S²/(Nn) < Var(WR) = (N − 1)S²/(Nn))
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Consider the following statements about the sample mean ȳ of a simple random sample:
1. ȳ is an unbiased estimator of the population mean under SRSWR.
2. ȳ is an unbiased estimator of the population mean under SRSWOR.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct. Under both SRSWR and SRSWOR, E(ȳ) = Ȳ.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Unit 10 Simple Random Sampling)
7.1Stratified & systematic samplingPractise this chapter · Set 1 free
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Match List I (design) with List II (key requirement or feature):
List I:
A. Stratified random sampling
B. Systematic sampling
C. Cluster sampling
D. Simple random sampling without replacement
List II:
1. An ordered list, a random start and a fixed interval
2. Stratum sizes known and a separate random sample from every stratum
3. Every possible sample of size n equally likely
4. Only a list of groups is needed; all units in the selected groups are studied
Select the correct answer using the code given below.
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Answer A. A-2, B-1, C-4, D-3
A-2, B-1, C-4, D-3. Cluster sampling enumerates whole selected groups; stratified sampling samples every stratum.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Units 11 Stratified and 12 Systematic Sampling)
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Consider the following statements:
1. Equal allocation is reasonable when the strata are of about the same size and variability.
2. Equal allocation always gives the smallest variance of ȳst.
Which of the statements given above is/are correct?
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Answer A. 1 only
Only 1. Equal allocation is close to optimum only when strata are alike in size and variability.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Units 11 Stratified and 12 Systematic Sampling)
Practise Sampling Techniques chapter by chapter. In the app every chapter is split into numbered sets of 20 questions, easier first, with your score on each set. Set 1 of every chapter is free.
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