SSC CGL Statistics – Sampling Theory – Exam-Level Drill
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Sampling units change at each stage (district → village → household); multiphase uses the same units with more information in later phases.
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SSC CGL Statistics – Sampling Theory – Exam-Level Drill – 12 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.
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1. Data tableHow many samples are there and what is the mean of their means?
Directions (Q 36–38): A population consists of the four values 4, 8, 12, 16. All possible samples of size 2 are drawn WITHOUT replacement (order ignored).
Correct Answer: D [6 samples; mean 10]
Explanation:
⁴C₂ = 6; means 6, 8, 10, 10, 12, 14 → average 10 = μ.
2.
(Use the directions above – Q 36–38)
Data tableThe variance of the sampling distribution of the mean is:
Data tableThe variance of the sampling distribution of the mean is:
Correct Answer: A [20/3]
Explanation:
σ² = 20; (20/2)(2/3) = 20/3 (direct: Σ(x̄ − 10)²/6 = 40/6).
3.
(Use the directions above – Q 36–38)
Data tableThe probability that the value 16 appears in the selected sample is:
Data tableThe probability that the value 16 appears in the selected sample is:
Correct Answer: D [1/2]
Explanation:
Inclusion probability = n/N = 2/4.
4.
Two independent large samples of sizes 25 and 36 come from populations with SDs 15 and 12. The SE of the difference of the sample means is:
Correct Answer: C [√13 ≈ 3.61]
Explanation:
√(15²/25 + 12²/36) = √(9 + 4) = √13.
5.
σ = 8. The smallest sample for which the mean is within ±2 of μ with 99% confidence (z = 2.576) is:
Correct Answer: B [107]
Explanation:
n = (2.576 × 8/2)² = 10.304² = 106.17 → 107 (62 would be the 95% answer).
6.
For N = 2,000 and n = 100, the finite population correction factor √((N − n)/(N − 1)) is about:
Correct Answer: A [0.9749]
Explanation:
√(1,900/1,999) ≈ 0.9749 – close to 1, so it is often ignored when n/N ≤ 5%.
7.
A survey must estimate a proportion within ±1 percentage point at 95% confidence with no prior estimate of P. The required n is:
Correct Answer: A [9604]
Explanation:
n = 1.96² × 0.25/0.01² = 0.9604/0.0001 = 9,604 (exact).
8.
Assertion–Reason
A: In systematic sampling with N = nk, the sample mean is an unbiased estimator of the population mean.
R: With a random start, every unit belongs to exactly one of the k possible samples, each chosen with probability 1/k.
A: In systematic sampling with N = nk, the sample mean is an unbiased estimator of the population mean.
R: With a random start, every unit belongs to exactly one of the k possible samples, each chosen with probability 1/k.
Correct Answer: C [Both A and R are true and R explains A]
Explanation:
Each unit lies in exactly one of the k samples, so the average of the k sample means is exactly the population mean.
9.
From 5 units, a sample of 2 is drawn WITH replacement. The probability that a particular unit appears at least once is:
Correct Answer: B [9/25]
Explanation:
1 − (4/5)² = 9/25 (slightly less than n/N = 2/5, because a unit can repeat).
10.
σ = 10, permitted error ±2. At 90% confidence (z = 1.645) the minimum sample size is:
Correct Answer: C [68]
Explanation:
(1.645 × 10/2)² = 8.225² = 67.65 → 68.
11.
Match the followingMatch the error with its type:
P. Wrong entries while copying schedules Q. Difference between x̄ and μ because only part of the population was studied R. Respondents refusing to answer
1. Sampling error 2. Non-response (non-sampling) error 3. Processing (non-sampling) error
P. Wrong entries while copying schedules Q. Difference between x̄ and μ because only part of the population was studied R. Respondents refusing to answer
1. Sampling error 2. Non-response (non-sampling) error 3. Processing (non-sampling) error
Correct Answer: B [P-3, Q-1, R-2]
Explanation:
Only Q comes from studying a part instead of the whole.
12.
A health survey first picks districts at random, then villages within the chosen districts, then households within the chosen villages. This design is:
Correct Answer: D [Multistage sampling]
Explanation:
Sampling units change at each stage (district → village → household); multiphase uses the same units with more information in later phases.
➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics
📘 SSC CGL 2026 – Statistics (Tier II Paper II)
Here you get the answer with a one-line explanation. 657 original questions with worked answers · notes, formulas, figures and statistical tables (z, t, χ², F) · practice sets + 3 mock tests
Get the book – ₹149 More quizzes
› SSC CGL Statistics – Mock Test M3 – Mixed Paper II Set (All 12 Chapters)
› SSC CGL Statistics – Mock Test M2 – Probability, Sampling, Inference & ANOVA (Chapters 6–10)
› SSC CGL Statistics – Mock Test M1 – Descriptive Statistics (Chapters 1–5)
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