Practice these 17 solved objective-type Statistics MCQs from the 2014 Lahore Board Inter Part 2, Paper II 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 normal distribution 95% of the area lies between the limits:
(A) μ ± 2σ (B) μ ± 1.96 σ (C) μ ± 1.645σ (D) μ ± 2.58σ
Correct Answer: (B) μ ± 1.96 σ — Under the normal distribution, exactly 95% of the area lies within μ ± 1.96σ.
2. In normal distribution μ = 10, σ² = 25 the mode is:
(A) 5 (B) 10 (C) 25 (D) 100
Correct Answer: (B) 10 — In a normal distribution, the mean, median and mode all coincide, so the mode equals μ = 10.
3. Normal distribution has parameters:
(A) μ (B) σ (C) σ² (D) μ, σ²
Correct Answer: (D) μ, σ² — The normal distribution is fully defined by its mean μ and variance σ², so these are its two parameters together.
4. A sample is a part of the:
(A) Sampling (B) Population (C) Unit (D) Error
Correct Answer: (B) Population — A sample is a smaller group selected from, and therefore a part of, the population.
5. A value calculated from population is called a:
(A) Statistic (B) Parameter (C) Mean (D) Proportion
Correct Answer: (B) Parameter — A numerical value computed from the entire population is called a parameter.
6. The standard error increases when the sample size is:
(A) Increased (B) Decreased (C) Fixed (D) Small
Correct Answer: (B) Decreased — Standard error = σ / √n, so it gets larger as the sample size n gets smaller.
7. If E(θ̂) = θ then θ̂ is:
(A) Biased (B) Unbiased (C) Positively biased (D) None of these
Correct Answer: (B) Unbiased — An estimator whose expected value equals the true parameter (E(θ̂) = θ) is, by definition, unbiased.
8. A judge acquits an innocent person. It is an example of:
(A) Type I error (B) Type II error (C) Correct decision (D) None of these
Correct Answer: (C) Correct decision — Acquitting a truly innocent person means correctly failing to reject a true null hypothesis (innocence), which is a correct decision.
9. The hypothesis which is to be tested for possible rejection is:
(A) Simple (B) Composite (C) Null (D) Alternative
Correct Answer: (C) Null — The null hypothesis is the statement that is directly tested and is either rejected or not rejected based on sample evidence.
10. In the regression line of y on x:
(A) Σx = Σx̂ (B) Σy = Σŷ (C) Σ(y − ŷ) = 0 (D) Both B and C
Correct Answer: (D) Both B and C — For the least squares regression line of y on x, both properties hold: the sum of actual y values equals the sum of predicted values, and the sum of residuals is always zero.
11. The regression line always passes through the points:
(A) (x, y) (B) (x̄, ȳ) (C) (x̄, y) (D) (x, ȳ)
Correct Answer: (B) (x̄, ȳ) — Every regression line passes through the point of means, (x̄, ȳ).
12. If both regression coefficients are negative, then the correlation coefficient will be:
(A) Negative (B) Positive (C) Zero (D) 1
Correct Answer: (A) Negative — Since r = ±√(b_yx × b_xy), the correlation coefficient always carries the same sign as the regression coefficients — if both are negative, r is negative too.
13. If the attributes A and B are completely associated, then the coefficient of association is equal to:
(A) 1 (B) Zero (C) −1 (D) None of these
Correct Answer: (A) 1 — Complete (positive) association between two attributes gives a coefficient of association equal to +1.
14. Both the coefficient of correlation and coefficient of association lies between:
(A) 0 and 1 (B) −1 and 0 (C) −1 and +1 (D) −2 and +2
Correct Answer: (C) −1 and +1 — Both the correlation coefficient and the coefficient of association always lie within the range −1 to +1, inclusive.
15. Suppose that y = 20 + 5x describes well an annual time series for 1992–2000. If the origin is 1996, then the trend value for 1997 is:
(A) 5 (B) 20 (C) 25 (D) 15
Correct Answer: (C) 25 — With origin at 1996, x for 1997 = 1997 − 1996 = 1. So y = 20 + 5(1) = 25.
16. Long term variations are regarded as:
(A) Secular trend (B) Seasonal variation (C) Cyclical variation (D) Irregular variation
Correct Answer: (A) Secular trend — Gradual, long-term movements in a time series over many years are called the secular trend.
17. Wall clock is an example of a:
(A) Digital Computer (B) Analog computer (C) Disk (D) None of these
Correct Answer: (B) Analog computer — A wall clock with continuously moving hands measures time on a continuous scale, making it an example of an analog computer/device.
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