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100+ Free Tamil Nadu HSE Second Year Statistics Practice Questions

Tamil Nadu Higher Secondary Second Year (HSE +2 / Class 12) Statistics under the Directorate of Government Examinations (DGE), Tamil Nadu practice questions are available now; exam metadata is being verified.

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2026 Statistics

Key Facts: Tamil Nadu HSE Second Year Statistics Exam

10:00–1:15

Official March 2026 HSE+2 theory sitting window including reading/verification time (dge.tn.gov.in timetable)

DGE TN HSE+2 March 2026 public examination timetable

35/100

Minimum pass mark per subject under the HSE new pattern, subject to theory/practical floor rules

DGE HSE_E.pdf scheme of examination

3 hours

Approximate theory writing duration after reading and particulars verification in the public exam schedule

DGE TN HSE+2 March 2026 timetable

DGE TN

Administered by the Directorate of Government Examinations, Chennai, for Tamil Nadu State Board Higher Secondary

dge.tn.gov.in

SCERT syllabus

Class 12 Statistics textbooks and syllabus prescribed by SCERT / School Education Department (Samacheer Kalvi)

DGE HSE scheme — syllabus prescribed by SCERT/DSE

English MCQ bank

This practice set is an English-language MCQ study adaptation, not the official mixed written paper

OpenExamPrep practice-content policy

₹150/₹200

School exam fee band for groups without/with practical subjects plus certificate/service charges (concessions apply)

DGE HSE_E.pdf school candidate fee table

March 2026

HSE Second Year public theory examinations scheduled 2–26 March 2026 with practicals 9–14 February 2026

DGE TN official timetable PDF 04.11.2025

Free English MCQ practice for Tamil Nadu HSE +2 Statistics (DGE). Official paper is mixed written theory on the Samacheer Kalvi Class 12 Statistics syllabus — this bank is a study adaptation, not a format simulation.

Sample Tamil Nadu HSE Second Year Statistics Practice Questions

Try these sample questions to test your Tamil Nadu HSE Second Year Statistics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In hypothesis testing, the hypothesis that is tested for possible rejection is called the:
A.Null hypothesis
B.Alternative hypothesis
C.Composite hypothesis only
D.Research hypothesis only
Explanation: The null hypothesis (H₀) is the statement tested for possible rejection under the sampling evidence. The alternative (H₁) is accepted only if H₀ is rejected.
2A Type I error occurs when the statistician:
A.Accepts a true alternative hypothesis
B.Rejects a true null hypothesis
C.Accepts a false null hypothesis
D.Rejects a false null hypothesis
Explanation: A Type I error is rejecting H₀ when H₀ is actually true. Its probability is controlled by the significance level α.
3If the level of significance is 5%, then the probability of Type I error is:
A.0.01
B.0.50
C.0.05
D.0.95
Explanation: The level of significance α is the probability of Type I error. At 5% significance, α = 0.05.
4For a large sample, the standard error of the sample mean x̄ when the population SD σ is known is:
A.σ / n
B.s / n
C.σ² / √n
D.σ / √n
Explanation: By the central limit theorem, for large n the sampling distribution of x̄ has SE = σ/√n when σ is known.
5A random sample of size 100 is drawn from a population with σ = 10. The standard error of the sample mean is:
A.1
B.10
C.0.1
D.100
Explanation: SE(x̄) = σ/√n = 10/√100 = 10/10 = 1.
6For testing H₀: μ = μ₀ against H₁: μ ≠ μ₀ using a large sample with known σ, the test statistic is:
A.z = (x̄ − μ₀) · √n
B.z = (x̄ − μ₀) / (σ/√n)
C.z = (x̄ − μ₀) / σ
D.t = (x̄ − μ₀) / (s/√n) only
Explanation: The large-sample z-test for a mean uses z = (x̄ − μ₀)/(σ/√n), which standardizes the sample mean under H₀.
7A sample of 64 observations has mean 52. The population SD is 8. To test H₀: μ = 50 against a two-sided alternative at 5%, the absolute value of z is approximately:
A.1.00
B.4.00
C.2.00
D.0.25
Explanation: z = (52 − 50)/(8/√64) = 2/(8/8) = 2/1 = 2. At 5% two-sided, critical |z| ≈ 1.96, so |z| = 2 is just significant.
8For a large sample proportion test, if n = 400 and p̂ = 0.45 under H₀: P = 0.40, the absolute value of z is approximately:
A.1.25
B.0.50
C.4.00
D.2.04
Explanation: SE under H₀ is √[P(1−P)/n] = √[0.4·0.6/400] = √(0.24/400) = √0.0006 ≈ 0.0245. z = (0.45−0.40)/0.0245 ≈ 2.04.
9When testing the difference of two large-sample means with known σ₁ and σ₂, the SE of (x̄₁ − x̄₂) is:
A.√(σ₁²/n₁ + σ₂²/n₂)
B.σ₁/n₁ + σ₂/n₂
C.√(σ₁² + σ₂²)/(n₁ + n₂)
D.(σ₁ + σ₂)/√(n₁ + n₂)
Explanation: For independent samples, Var(x̄₁ − x̄₂) = σ₁²/n₁ + σ₂²/n₂, so SE = √(σ₁²/n₁ + σ₂²/n₂).
10A critical region of a test is the set of sample outcomes that lead to:
A.Estimation of σ only
B.Rejection of H₀
C.Acceptance of H₀ only
D.No decision
Explanation: The critical (rejection) region consists of those values of the test statistic for which H₀ is rejected at the chosen α.

About the Tamil Nadu HSE Second Year Statistics Practice Questions

Verified exam format metadata for Tamil Nadu Higher Secondary Second Year (HSE +2 / Class 12) Statistics under the Directorate of Government Examinations (DGE), Tamil Nadu is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.