Practice these 17 solved objective-type Statistics MCQs from the 2013 Lahore Board Inter Part 2, Paper I 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. The probability of rejecting Null Hypothesis when it is false is:
(A) Error (B) Type-I error (C) Type-II error (D) Power of test
Correct Answer: (D) Power of test — The probability of correctly rejecting a false null hypothesis is called the power of the test.
2. Printer, monitor, scanner and plotter are the:
(A) Input devices (B) Output devices (C) Processing devices (D) Storage devices
Correct Answer: (B) Output devices — Printer, monitor and plotter are output devices. (Note: a scanner is technically an input device — this grouping matches the paper's intended answer, but it's worth double-checking against your official answer key.)
3. The value of r_xy is always between:
(A) −1 and +1 (B) −∞ and 0 (C) 0 and +1 (D) 0 and +∞
Correct Answer: (A) −1 and +1 — The correlation coefficient r_xy always lies within the range −1 to +1, inclusive.
4. For the standard normal distribution P (Z > mean) is:
(A) Less than 0.5 (B) More than 0.5 (C) Equal to 0.5 (D) Equal to one
Correct Answer: (C) Equal to 0.5 — Since the standard normal curve is symmetric about its mean, exactly half the area lies above the mean.
5. An estimator θ̂ is said to be unbiased estimator of θ if:
(A) E(θ̂) = θ (B) E(θ̂) > θ (C) E(θ̂) < θ (D) E(θ̂) ≠ θ
Correct Answer: (A) E(θ̂) = θ — An estimator is unbiased when its expected value exactly equals the true parameter it is estimating.
6. In the regression equation X = a + bY, X is called:
(A) Dependent variable (B) Independent variable (C) Qualitative variable (D) Quantitative variable
Correct Answer: (A) Dependent variable — Since X is expressed as a function of Y (X = a + bY), X is the variable being predicted, making it the dependent variable.
7. ∫ (from −∞ to ∞) f(x) dx is always equal to:
(A) Zero (B) One (C) f(x) + 1 (D) E(x)
Correct Answer: (B) One — The total area under any probability density function, integrated over its entire range, always equals 1.
8. The sum of squares of residuals is denoted by:
(A) e (B) Σe (C) Σe² (D) Σe²/n
Correct Answer: (C) Σe² — The sum of squares of residuals is denoted Σe², and least squares regression minimizes exactly this quantity.
9. When the production of a thing is decreasing, this stage is called as:
(A) Recession (B) Recovery (C) Boom (D) Depression
Correct Answer: (A) Recession — The stage of the business cycle where production and economic activity begin to decline is called recession.
10. In sampling without replacement, an element can be chosen:
(A) More than twice (B) More than once (C) Less than (D) Only once
Correct Answer: (D) Only once — Without replacement, once a unit is selected it is not returned to the population, so it can be chosen only once.
11. The value of χ² statistics is always:
(A) Positive (B) Negative (C) One (D) Zero
Correct Answer: (A) Positive — Since χ² is a sum of squared standardized deviations, its value is always positive (non-negative).
12. The term sample space is used for:
(A) All possible outcomes (B) Sample (C) Probability (D) Sample design
Correct Answer: (A) All possible outcomes — The sample space is defined as the set of all possible outcomes of a random experiment.
13. Regression coefficient is independent of:
(A) Units of measurement (B) Scale and origin (C) Scale only (D) Both A and B
Correct Answer: (B) Scale and origin — Per the standard textbook rule tested here, the regression coefficient is treated as independent of both scale and origin. (Note: strictly speaking, the regression coefficient is independent of origin but does change with scale — worth verifying against your official answer key.)
14. If X is N (μ, σ²), the percentage of the area contained within the limits μ ± 3σ is:
(A) 50% (B) 68.27% (C) 95.45% (D) 99.73%
Correct Answer: (D) 99.73% — Under the empirical rule, the interval μ ± 3σ covers approximately 99.73% of the area under the normal curve.
15. If the magnitude of calculated value of "t" is less than the tabulated value of "t" and alternative hypothesis is two sided, we should:
(A) Reject H₀ (B) Not reject H₀ (C) Reject H₁ (D) Accept H₁
Correct Answer: (B) Not reject H₀ — When the calculated test statistic is smaller than the critical (tabulated) value, there isn't enough evidence to reject the null hypothesis.
16. If (AB) = (A)(B)/n, the two attributes A and B are:
(A) Independent (B) Correlated (C) Dependent (D) Quantitative
Correct Answer: (A) Independent — The condition (AB) = (A)(B)/n is precisely the definition of independence between two attributes.
17. A population about which we want to get some information is called:
(A) Finite population (B) Infinite population (C) Sample population (D) Target population
Correct Answer: (D) Target population — The population that is the actual focus of a study, about which conclusions are to be drawn, is called the target population.
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