Practice these 17 solved objective-type Statistics MCQs covering hypothesis testing, correlation, sampling, and normal distribution. Each question below includes the verified correct answer and a short explanation. Scroll down to attempt the interactive quiz version with instant scoring.
1. If H₀ is true and we reject it then it is called:
(A) Type I error (B) Type II error (C) Standard error (D) Sampling error
Correct Answer: (A) Type I error — Rejecting a null hypothesis when it is actually true is defined as a Type I error.
2. One byte is equal to:
(A) 8 bits (B) 4 bits (C) 6 bits (D) 12 bits
Correct Answer: (A) 8 bits — By definition, one byte consists of 8 bits.
3. If r_xy = 0.75 the correlation co-efficient between u = 1.5x and v = 2y i.e. r_uv is:
(A) Zero (B) 0.75 (C) −0.75 (D) 1.5
Correct Answer: (B) 0.75 — Multiplying variables by positive constants does not change the correlation coefficient, so r_uv remains 0.75.
4. The range of normal distribution is:
(A) 0 to +∞ (B) −∞ to 0 (C) −∞ to +∞ (D) 0 to n
Correct Answer: (C) −∞ to +∞ — The normal distribution extends over the entire real number line, from −∞ to +∞.
5. Which of the following is biased estimator:
(A) X̄ = ΣX/n (B) p̂ = X/n (C) s² = Σ(X−X̄)²/(n−1) (D) S² = Σ(X−X̄)²/n
Correct Answer: (D) S² = Σ(X−X̄)²/n — Dividing the sum of squared deviations by n (instead of n−1) systematically underestimates the population variance, making S² a biased estimator.
6. When b_xy is positive then b_yx will be:
(A) Negative (B) Positive (C) Zero (D) One
Correct Answer: (B) Positive — Both regression coefficients always carry the same sign, so if b_xy is positive, b_yx is also positive.
7. In a normal curve μ ± 2σ covers:
(A) 50% area (B) 68.27% area (C) 95.45% area (D) 99.73% area
Correct Answer: (C) 95.45% area — Under the empirical rule, the interval μ ± 2σ covers approximately 95.45% of the area under the normal curve.
8. A second degree parabola has:
(A) One constant (B) Two constants (C) Three constants (D) No constant
Correct Answer: (C) Three constants — A second degree parabola, y = a + bx + cx², has three constants: a, b, and c.
9. A business cycle has:
(A) One stage (B) Two stages (C) Three stages (D) Four stages
Correct Answer: (D) Four stages — A business cycle consists of four stages: prosperity, recession, depression, and recovery.
10. The standard deviation of any sampling distribution is called:
(A) Standard error (B) Non-sampling error (C) Type-I error (D) Biased error
Correct Answer: (A) Standard error — The standard deviation of a statistic's sampling distribution is called its standard error.
11. The order of (ABC) is:
(A) 1 (B) 2 (C) 3 (D) Zero
Correct Answer: (C) 3 — The order of a class frequency equals the number of attributes involved; since (ABC) involves three attributes A, B and C, its order is 3.
12. If X̄ = 10 and μ = 12 then sampling error is equal to:
(A) 22 (B) 10 (C) −2 (D) 12
Correct Answer: (C) −2 — Sampling error = X̄ − μ = 10 − 12 = −2.
13. The value of the co-efficient of correlation "r" lies between:
(A) 0 and 1 (B) −1 and 0 (C) −1 and +1 (D) −0.5 and +0.5
Correct Answer: (C) −1 and +1 — The correlation coefficient r always lies within the range −1 to +1, inclusive.
14. The shape of the curve of normal distribution is:
(A) Lepto-kurtic (B) Platy-kurtic (C) Skewed (D) Meso-kurtic
Correct Answer: (D) Meso-kurtic — The standard bell-shaped normal curve has kurtosis β₂ = 3, which is classified as mesokurtic.
15. A hypothesis may be classified as:
(A) Simple (B) Composite (C) Null (D) All of these
Correct Answer: (D) All of these — Hypotheses can be classified as simple, composite, or null, so all of these are valid classifications.
16. Two attributes A and B are independent if (AB) =:
(A) (A)(B) / N (B) (α)(β) / N (C) (A)(Γ) / N (D) (α)(B) / N
Correct Answer: (A) (A)(B) / N — Two attributes A and B are independent when the observed frequency (AB) equals the expected frequency under independence: (A)(B) / N.
17. In sampling with replacement, the following is always true:
(A) n = N (B) n < N (C) n > N (D) All of these
Correct Answer: (C) n > N — Since replacement allows the same unit to be drawn again, the sample size n is not restricted by the population size N and can exceed it — unlike sampling without replacement, where n can never exceed N.
Now try the interactive version of this quiz below to test your score instantly:
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