SSC CGL Statistics – Statistical Inference – Estimation & Testing of Hypotheses – Level 1 · Warm-up
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z = (102 − 100)/(8/√64) = 2/1 = 2.
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SSC CGL Statistics – Statistical Inference – Estimation & Testing of Hypotheses – Level 1 · Warm-up – 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.
A Type I error is committed when we:
Correct Answer: D [Reject H₀ when H₀ is true]
Explanation:
Type I = rejecting a true null hypothesis (false alarm).
2.
The level of significance α of a test is the probability of:
Correct Answer: B [Type I error]
Explanation:
Answer: Type I error. α = P(reject H₀ | H₀ true).
3.
If the probability of a Type II error is β, the power of the test is:
Correct Answer: C [1 − β]
Explanation:
Power = P(reject H₀ | H₀ false) = 1 − β.
4.
Which is an unbiased estimator of the population variance σ² from a random sample x₁, …, xₙ?
Correct Answer: A [Σ(x − x̄)²/(n − 1)]
Explanation:
Divisor n − 1 makes E(s²) = σ²; divisor n underestimates by the factor (n − 1)/n.
5.
x̄ = 40, σ = 5 and n = 25. The 95% confidence interval for μ is:
Correct Answer: A [38.04 to 41.96]
Explanation:
Answer: 38.04 to 41.96. SE = 5/5 = 1; 40 ± 1.96 × 1.
6.
A t-test for a single mean uses a sample of 12 observations. The degrees of freedom are:
Correct Answer: B [11]
Explanation:
Answer: 11. df = n − 1 = 11.
7.
For a χ² test of independence in a 3 × 4 contingency table, the degrees of freedom are:
Correct Answer: C [6]
Explanation:
Answer: 6. (r − 1)(c − 1) = 2 × 3 = 6.
8.
The critical value of z for a two-tailed test at the 1% level is:
Correct Answer: D [2.576]
Explanation:
1% split into two tails of 0.5% → z = 2.576.
9.
Statement-basedWhich is/are correct?
I. A consistent estimator gets closer to the parameter as n increases.
II. Every unbiased estimator is consistent.
I. A consistent estimator gets closer to the parameter as n increases.
II. Every unbiased estimator is consistent.
Correct Answer: B [Only I]
Explanation:
X₁ alone is unbiased for μ but its variance never falls – not consistent.
10.
Fill in the blankThe F statistic is the ratio of two independent estimates of the population ______.
Correct Answer: D [variance]
Explanation:
Answer: variance. F = s₁²/s₂².
11.
Match the followingMatch the test with its use:
P. t-test Q. χ²-test R. F-test
1. equality of two variances 2. goodness of fit 3. mean of a small sample, σ unknown
P. t-test Q. χ²-test R. F-test
1. equality of two variances 2. goodness of fit 3. mean of a small sample, σ unknown
Correct Answer: A [P-3, Q-2, R-1]
Explanation:
t for small-sample means, χ² for fit/independence, F for variances.
12.
H₀: μ = 100. A sample of 64 gives x̄ = 102; σ = 8. The value of the test statistic z is:
Correct Answer: C [2]
Explanation:
z = (102 − 100)/(8/√64) = 2/1 = 2.
➤ 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
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› SSC CGL Statistics – Mock Test M1 – Descriptive Statistics (Chapters 1–5)
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