Statistics MCQs 2015 – Lahore Board, Inter Part 2

Practice these 17 solved objective-type Statistics MCQs from the 2015 Lahore Board Inter Part 2 exam. Each question below includes the verified correct answer and a short explanation. Scroll down to attempt the interactive quiz version with instant scoring.

1. In a normal distribution, X lies between:

(A) −∞ and 0 (B) −∞ and ∞ (C) 0 and ∞ (D) −1 and +1

Correct Answer: (B) −∞ and ∞ — The normal distribution extends over the entire real number line, from −∞ to +∞.

2. If Z ~ N (0, 1), then μ₄ is equal to:

(A) 0 (B) 1 (C) 3 (D) σ⁴

Correct Answer: (C) 3 — For a standard normal distribution, the fourth central moment μ₄ = 3σ⁴ = 3(1)⁴ = 3.

3. In a normal distribution, mean deviation is approximately:

(A) 2/3 (B) 2/3 σ (C) 4/5 (D) 4/5 σ

Correct Answer: (D) 4/5 σ — The mean deviation of a normal distribution is approximately 0.7979σ, which is closest to 4/5σ (0.8σ).

4. Sample is a subset of:

(A) Population (B) Data (C) Set (D) Distribution

Correct Answer: (A) Population — A sample is a smaller group selected from, and therefore a subset of, the population.

5. In sampling without replacement, the number of samples is equal to:

(A) n (B) N (C) Nⁿ (D) (N choose n)

Correct Answer: (D) (N choose n) — Without replacement, the number of possible samples of size n from a population of size N is given by the combination formula, N choose n.

6. Σ X̄ P(X̄) is equal to:

(A) n (B) μ_p̂ (C) μ_x̄ (D) N

Correct Answer: (C) μ_x̄ — Σ X̄ P(X̄) is, by definition, the mean of the sampling distribution of X̄, denoted μ_x̄.

7. The estimator of μ is:

(A) X̄ (sample mean) (B) x (a single observation) (C) σ (standard deviation) (D) None of these

Correct Answer: (A) X̄ (sample mean) — The sample mean X̄ is used as the standard estimator of the population mean μ.

8. Level of confidence is denoted by:

(A) α (B) β (C) 1 − α (D) 1 − β

Correct Answer: (C) 1 − α — The level of confidence, representing the probability that the interval contains the true parameter, is denoted 1 − α.

9. Which of the following is not composite hypothesis:

(A) μ ≥ μ₀ (B) μ ≤ μ₀ (C) μ = μ₀ (D) μ ≠ μ₀

Correct Answer: (C) μ = μ₀ — μ = μ₀ specifies one exact value, making it a simple hypothesis — not composite. The other options cover a range of values, making them composite.

10. In the regression ŷ = a + bx, the y is called:

(A) Independent variable (B) Dependent variable (C) Fix variable (D) Constant

Correct Answer: (B) Dependent variable — In regression, y is the variable being predicted/explained, so it is called the dependent variable.

11. In the regression ŷ = a + bx:

(A) Σx = Σx̂ (B) Σy = Σŷ (C) Σx = Σy (D) x = y

Correct Answer: (B) Σy = Σŷ — A key property of the least squares regression line is that the sum of actual y values always equals the sum of predicted values.

12. The range of slope is:

(A) −1 to 1 (B) 0 to 1 (C) −∞ to ∞ (D) 0 to ∞

Correct Answer: (C) −∞ to ∞ — The slope of a regression line can theoretically take any real value.

13. If ( Σd² ) / ( n(n² − 1) ) is zero then value of rₛ is:

(A) 0.5 (B) −1 (C) 0 (D) 1

Correct Answer: (D) 1 — Spearman's formula is rₛ = 1 − 6Σd²/(n(n²−1)). If this fraction term is zero (Σd² = 0), then rₛ = 1 − 0 = 1.

14. The co-efficient of association (Q) lies between:

(A) 0 & +1 (B) −1 & +1 (C) −∞ to ∞ (D) −1 to 0

Correct Answer: (B) −1 & +1 — The coefficient of association Q always lies within the range −1 to +1, inclusive.

15. The graph of time series is called:

(A) Historigram (B) Histogram (C) Polygon (D) Circle

Correct Answer: (A) Historigram — A time series (values plotted against time) is graphically represented as a historigram.

16. Movements in secular trend are:

(A) Smooth (B) Steady (C) Regular (D) All of these

Correct Answer: (D) All of these — The secular trend represents the long-term, gradual movement in a time series, which is smooth, steady, and regular.