Statistics MCQs 2025 – Lahore Board Inter Part 2

Practice these 17 solved objective-type Statistics MCQs covering time series, hypothesis testing, regression, normal distribution, and sampling. Each question below includes the verified correct answer and a short explanation. Scroll down to attempt the interactive quiz version with instant scoring.

1. The systematic component of time series which follows regular pattern of variation is:

(A) Signal   (B) Noise   (C) Error   (D) Model

Correct Answer: (A) Signal — The systematic, regularly-repeating part of a time series is called the signal; the irregular, unpredictable part is the noise.

2. Which of the following is a simple hypothesis if u₀ = 10:

(A) μ < μ₀   (B) μ > μ₀   (C) μ ≠ μ₀   (D) μ = μ₀

Correct Answer: (D) μ = μ₀ — A simple hypothesis specifies one exact value of the parameter; the other options describe a range of values (composite hypotheses).

3. The standard error increases as the sample size is:

(A) Not changed   (B) Increased   (C) Fixed   (D) Decreased

Correct Answer: (D) Decreased — Standard error = σ/√n, so it gets larger as the sample size n gets smaller.

4. The regression line always passes through the point:

(A) (X̄, Ȳ)   (B) (μ, σ)   (C) (X, Y)   (D) (0, 1)

Correct Answer: (A) (X̄, Ȳ) — Every regression line passes through the point of means, (X̄, Ȳ).

5. Suppose that sample mean X̄ = 120 and upper limit of 90% confidence interval is 132. The lower limit will be:

(A) 112   (B) 190   (C) 30   (D) 108

Correct Answer: (D) 108 — A confidence interval is symmetric about the mean: margin of error = 132 − 120 = 12, so lower limit = 120 − 12 = 108.

6. In normal distribution P (−∞ < X < ∞) is equal to:

(A) 0   (B) ∞   (C) 1   (D) −∞

Correct Answer: (C) 1 — The total area under any probability distribution curve, covering all possible values, always equals 1.

7. If (A) = 60, (B) = 40 and (AB) = 24, n = 100 then A and B are called:

(A) Positively associated   (B) Negatively associated   (C) Independent attributes   (D) Skewed

Correct Answer: (C) Independent attributes — Expected frequency under independence = (A)(B)/n = (60 × 40)/100 = 24, which matches the actual (AB) = 24, confirming independence.

8. A population which consists of unlimited number of elements is called:

(A) Finite population   (B) Infinite population   (C) Sampled population   (D) Composite population

Correct Answer: (B) Infinite population — A population with no fixed, countable limit on the number of elements is called infinite.

9. The sum of squares of residuals Σe² is always:

(A) Zero   (B) Minimum   (C) Maximum   (D) One

Correct Answer: (B) Minimum — The least squares method fits a regression line specifically to minimize Σe².

10. Normal distribution has maximum ordinate at its:

(A) Q.D.   (B) S.D.   (C) M.D.   (D) Mean

Correct Answer: (D) Mean — The normal curve is symmetric and bell-shaped, peaking exactly at the mean.

11. Independent variable is also called a:

(A) Constant   (B) Regressand   (C) Not fixed   (D) Regressor

Correct Answer: (D) Regressor — In regression analysis, the independent (predictor) variable is called the regressor; the dependent variable is the regressand.

12. In standard normal distribution standard deviation is always:

(A) 0   (B) 2   (C) 1   (D) −1

Correct Answer: (C) 1 — The standard normal distribution is defined to have mean 0 and standard deviation exactly 1.

13. The brain of the computer is known as:

(A) ALU   (B) ROM   (C) RAM   (D) CPU

Correct Answer: (D) CPU — The Central Processing Unit carries out instructions and controls all operations, so it is called the brain of the computer.

14. If b_yx = −0.75, b_xy = −0.33 then the correlation coefficient r is:

(A) 0.5   (B) 0   (C) 1   (D) −0.5

Correct Answer: (D) −0.5 — r = ±√(b_yx × b_xy) = ±√(0.75 × 0.33) ≈ ±0.5. Since both regression coefficients are negative, r is negative: r = −0.5.

15. For a (5 × 4) contingency table, degree of freedom is:

(A) 15   (B) 20   (C) 12   (D) 9

Correct Answer: (C) 12 — Degrees of freedom = (rows − 1)(columns − 1) = (5 − 1)(4 − 1) = 4 × 3 = 12.

16. Rejecting H₀ when H₀ is true is a:

(A) Type-I error   (B) Type-II error   (C) Correct decision   (D) Standard error

Correct Answer: (A) Type-I error — Incorrectly rejecting a true null hypothesis is defined as a Type-I error.

17. The simple random sampling is a type of --- sampling:

(A) Probability   (B) Non-probability   (C) Infinite   (D) Quantity

Correct Answer: (A) Probability — In simple random sampling, every element has a known, equal chance of selection, making it a probability sampling method.

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