All Free Quantitative Methods MCQs with Answers
Every Quantitative Methods question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.
360 questions · page 17 of 18
- A. Stratified sampling
- B. Systematic sampling
- C. Purposive sampling
- D. Convenience sampling
Explanation: Purposive sampling deliberately selects units with particular characteristics or knowledge relevant to the research.
Correct answer: Purposive sampling- A. Judgement sampling
- B. Quota sampling
- C. Simple random sampling
- D. Multistage sampling
Explanation: Multistage sampling selects samples through two or more successive stages.
Correct answer: Multistage sampling- A. 0.0049
- B. 0.0240
- C. 0.0490
- D. 0.4000
Explanation: The standard error is calculated as the square root of p(1 minus p) divided by n. Thus, √(0.40 × 0.60 ÷ 100) is approximately 0.0490.
Correct answer: 0.0490- A. 196
- B. 256
- C. 385
- D. 400
Explanation: When no prior proportion is available, p = 0.50 is used because it gives the maximum variance.
Correct answer: 385- A. Highest population value
- B. Largest sample mean
- C. Smallest variance
- D. Greatest sampling fraction
Explanation: Efficiency among unbiased estimators is judged by variance. The estimator with the smallest variance produces the most precise estimates…
Correct answer: Smallest variance- A. Researchers select entire groups and survey their members
- B. Researchers select every kth unit after a random start
- C. Researchers randomly choose units from each subgroup
- D. Researchers fill preset subgroup quotas without requiring random selection
Explanation: Quota sampling sets required numbers for selected categories, but the units within those categories are usually chosen nonrandomly.
Correct answer: Researchers fill preset subgroup quotas without requiring random selection- A. With replacement from the observed sample
- B. Without replacement from the population
- C. From every population unit exactly once
- D. Only from units with missing responses
Explanation: Bootstrap resampling repeatedly draws, with replacement, from the observed sample to approximate the sampling distribution of a statistic.
Correct answer: With replacement from the observed sample- A. There is a 95 percent probability that the fixed parameter lies in this calculated interval
- B. About 95 percent of similarly constructed intervals contain the fixed parameter
- C. Exactly 95 percent of population values lie inside the calculated interval
- D. The sample statistic has a 95 percent probability of equalling the parameter
Explanation: In repeated sampling, about 95 percent of intervals constructed by the same method contain the fixed population parameter.
Correct answer: About 95 percent of similarly constructed intervals contain the fixed parameter- A. Population size only
- B. Within stratum variability only
- C. Sampling frame code
- D. Product of size and variability
Explanation: Neyman allocation considers both the size of a stratum and its within stratum standard deviation.
Correct answer: Product of size and variability- A. Precision
- B. Unbiasedness
- C. Representativeness
- D. Randomization
Explanation: An estimator can be unbiased while still having high variance. Reducing its spread improves precision, whereas unbiasedness concerns…
Correct answer: Precision- A. 1
- B. 2
- C. 3
- D. 4
Explanation: Adding the two equations gives 3x = 9, so x = 3. Substituting this value into either equation gives y = 1.
Correct answer: 3- A. 1
- B. 2
- C. 3
- D. 6
Explanation: The second equation is three times the equation x + 2y = 4. Therefore, the first equation must be x + 2y = 4, which requires a = 1.
Correct answer: 1- A. -26
- B. -14
- C. 14
- D. 26
Explanation: The coefficient matrix is [[4, 3], [2, -5]]. Its determinant is (4 × -5) - (3 × 2) = -20 - 6 = -26.
Correct answer: -26- A. 2 × 4
- B. 3 × 3
- C. 4 × 2
- D. 2 × 3
Explanation: The inner dimensions, 3 and 3, agree, so multiplication is possible. The product takes its outer dimensions, giving a 2 × 4 matrix.
Correct answer: 2 × 4- A. [[2, -1], [-3, 2]]
- B. [[2, -1], [-3, 1]]
- C. [[1, -1], [-3, 2]]
- D. [[2, 1], [3, 2]]
Explanation: The determinant is (2 × 2) - (1 × 3) = 1. Interchanging the diagonal entries and changing the signs of the other entries gives [[2, -1]…
Correct answer: [[2, -1], [-3, 1]]- A. x = 2, y = 2, z = 2
- B. x = 3, y = 1, z = 2
- C. x = 1, y = 3, z = 2
- D. x = 2, y = 1, z = 3
Explanation: Subtracting the second equation from the first gives 2z = 4, so z = 2. The remaining equations then give x + y = 4 and x - y = 2…
Correct answer: x = 2, y = 2, z = 2- A. k = 4 or -4
- B. k = -2 only
- C. k = 2 only
- D. k = 8 or -8
Explanation: A matrix is singular when its determinant is zero. Here, k² - 16 = 0, so k² = 16 and k = 4 or k = -4.
Correct answer: k = 4 or -4- A. X = AB
- B. X = A⁻¹B
- C. X = BA
- D. X = B⁻¹A
Explanation: Premultiplying AX = B by A⁻¹ gives A⁻¹AX = A⁻¹B. Since A⁻¹A is the identity matrix, X = A⁻¹B.
Correct answer: X = A⁻¹B- A. The system has a unique solution
- B. The system is inconsistent
- C. The system has infinitely many solutions
- D. The coefficient matrix is an identity matrix
Explanation: The row represents the equation 0 = 5, which is impossible. Therefore, the system is inconsistent and has no solution, not infinitely many…
Correct answer: The system is inconsistent- A. The equations have no solution
- B. The equations have infinitely many solutions
- C. The equations have exactly one solution
- D. The equations are necessarily identical
Explanation: A nonzero coefficient determinant means the coefficient matrix is nonsingular.
Correct answer: The equations have exactly one solution