SSC CGL Statistics – Statistical Inference – Estimation & Testing of Hypotheses – Level 3 · Challenge

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SSC CGL Statistics – Statistical Inference – Estimation & Testing of Hypotheses – Level 3 · Challenge – 8 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 coin is tossed 10 times and H₀: p = 1/2 is rejected if 9 or more heads appear. The size α of the test is:

Correct Answer: C [11/1024]

Explanation:

Answer: 11/1024. (¹⁰C₉ + ¹⁰C₁₀)/2¹⁰ = 11/1024.

2.  
For the test in the previous question, if the true p is 0.8, the probability of a Type II error is about:

Correct Answer: A [0.6242]

Explanation:

β = P(X ≤ 8 | p = 0.8) = 1 − [10(0.8)⁹(0.2) + 0.8¹⁰] ≈ 0.6242.

3.  
Statement-basedA test gives p-value = 0.03. Which is/are correct?
I. H₀ is rejected at the 5% level.
II. H₀ is rejected at the 1% level.

Correct Answer: C [Only I]

Explanation:

Reject when p-value < α: 0.03 < 0.05 but 0.03 > 0.01.

4.  
Other things fixed, the sample size is increased from 100 to 400. The width of a confidence interval for μ becomes:

Correct Answer: D [half]

Explanation:

Answer: half. Width ∝ 1/√n: √(400/100) = 2.

5.  
n = 9, s² = 45 (divisor n − 1). Test H₀: σ² = 25 against H₁: σ² > 25 at 5% (χ²₀.₀₅, 8 df = 15.507):

Correct Answer: B [χ² = 14.4; do not reject H₀]

Explanation:

χ² = (n − 1)s²/σ₀² = 8 × 45/25 = 14.4 < 15.507.

6.  
A sample 3, 5, 7, 9 comes from a uniform distribution on (0, θ). The method-of-moments estimate of θ is:

Correct Answer: D [12]

Explanation:

E(X) = θ/2 → θ̂ = 2x̄ = 2 × 6 = 12.

7.  
A sample correlation r = 0.6 is found from n = 18 pairs. The statistic t = r√(n − 2)/√(1 − r²) and the conclusion at 5% (t₀.₀₂₅(16) = 2.120) are:

Correct Answer: A [t = 3; significant correlation]

Explanation:

Answer: t = 3; significant correlation. t = 0.6 × 4/0.8 = 3 > 2.120.

8.  
Arrange in orderArrange in increasing order: (i) z₀.₀₂₅ (ii) t₀.₀₂₅ with 30 df (iii) t₀.₀₂₅ with 5 df (iv) z₀.₀₀₅

Correct Answer: B [(i), (ii), (iii), (iv)]

Explanation:

1.960 < 2.042 < 2.571 < 2.576 – t with 5 df is just below the 1% z value.

➤ 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
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