SSC CGL Statistics – Sampling Theory – Level 2 · Exam Level · Paper II Sprint

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SSC CGL Statistics – Sampling Theory – Level 2 · Exam Level · Paper II Sprint – 15 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.  
A population of 41 units has σ² = 64. For a simple random sample of 16 drawn without replacement, the variance of the sample mean is:

Correct Answer: B [5/2]

Explanation:

(σ²/n)(N − n)/(N − 1) = (64/16)(25/40) = 2.5.

2.  
In a large population 25% of households own a car. The standard error of the sample proportion for a sample of 75 households is:

Correct Answer: D [0.05]

Explanation:

√(PQ/n) = √(0.25 × 0.75/75) = √0.0025 = 0.05.

3.  
A college has 1,500 arts, 1,000 science and 1,500 commerce students. With proportional allocation, a stratified sample of 80 takes how many science students?

Correct Answer: A [20]

Explanation:

n_h = n × N_h/N = 80 × 1,000/4,000 = 20.

4.  
Two strata have sizes 2,000 and 500 and standard deviations 2 and 2. Under Neyman allocation, a total sample of 100 gives the first stratum:

Correct Answer: C [80]

Explanation:

Equal SDs → Neyman = proportional: 100 × 4,000/5,000 = 80.

5.  
The SE of a sample mean is 6 when n = 36. To make the SE 2 (same population, large), the sample size must be:

Correct Answer: C [324]

Explanation:

Square Law: SE ÷ 3 → n × 3² = 36 × 9 = 324.

6.  
The SD of a population is 20. What is the minimum sample size so that the sample mean is within 4 of μ with 95% confidence?

Correct Answer: A [97]

Explanation:

n = (1.96 × 20/4)² = 9.8² = 96.04 → round UP to 97.

7.  
With no prior idea of the proportion P, what sample size gives a margin of error of 0.04 at 95% confidence?

Correct Answer: B [601]

Explanation:

Take P = 0.5: n = 1.96² × 0.25/0.04² = 600.25 → 601.

8.  
Two-quantity comparison
Quantity I: number of samples of size 3 drawn with replacement (order counted) from 5 units
Quantity II: 10 × number of samples of size 3 drawn without replacement (order ignored) from 5 units

Correct Answer: D [Quantity I > Quantity II]

Explanation:

QI = 5³ = 125; QII = 10 × ⁵C₃ = 100.

9.  
In simple random sampling without replacement from N units, the probability that a particular unit is included in a sample of size n is:

Correct Answer: A [n/N]

Explanation:

A given unit is in C(N − 1, n − 1) of the C(N, n) samples, and C(N − 1, n − 1)/C(N, n) = n/N (1/N is the chance at any one draw).

10.  
Assertion–Reason
A: Increasing the sample size always reduces non-sampling errors.
R: Non-sampling errors arise from measurement, response and processing.

Correct Answer: D [A is false but R is true]

Explanation:

Bigger surveys need more staff and handling, so non-sampling errors may even grow; R correctly lists their sources.

11.  
Trick Spotterσ = 30, n = 100, and the SE must be cut to one-third. The quickest correct thinking is:

Correct Answer: B [Multiply n by 3² → n = 900]

Explanation:

SE ∝ 1/√n, so the factor on n is the square of the factor on SE.

12.  
Spot My Mistake“σ = 18, n = 36, so SE of the mean = 18/36 = 0.5.” The correct SE is:

Correct Answer: C [3]

Explanation:

SE = σ/√n = 18/6 = 3 – the student divided by n instead of √n.

13.  
A list of 900 shops is numbered 1 to 900. A systematic sample of 30 uses a random start of 11. Which shop number is the 10th in the sample?

Correct Answer: B [281]

Explanation:

k = 900/30 = 30; 10th unit = 11 + 9 × 30 = 281.

14.  
Odd one outWhich of these sampling designs is the odd one out?

Correct Answer: D [Quota sampling]

Explanation:

The other three are probability methods; quota sampling has no random selection.

15.  
Diagram-basedThe population is split into groups and the shaded groups are taken completely.

Which statement describes this design correctly?

Correct Answer: A [Clusters are chosen at random and every unit in a chosen cluster is studied]

Explanation:

Cluster sampling = random choice of whole groups; sampling inside every group is stratified sampling.

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