All Free Statistics MCQs with Answers
Every Statistics question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.
545 questions · page 27 of 28
- A. Systematic sampling
- B. Cluster sampling
- C. Simple random sampling
- D. Stratified samplingDemographics
Explanation: Cluster sampling is commonly used when an individual-level sampling frame is unavailable but natural groups or geographic areas can be…
Correct answer: Cluster sampling- A. Close another
- B. Far a part
- C. Mixed
- D. None of these
Explanation: Cluster sampling is useful when individual units are geographically far apart, because selecting whole clusters reduces travel and…
Correct answer: Far a part- A. n > 30
- B. N(1 - p) > 5
- C. 2 n 5
- D. N < 30
Explanation: A common rule of thumb is that n greater than 30 makes the sampling distribution of the mean approximately normal, especially when the…
Correct answer: n > 30- A. ux - x2
- B. u1 - u2
- C. 6x - x2
- D. 6×2 - x2
Explanation: Expectation is linear, so E(X₁ − X₂) = E(X₁) − E(X₂) = μ₁ − μ₂. This remains true even when the two variables are not independent.
Correct answer: u1 - u2- A. Standard error of statistics
- B. Sampling error of statistics
- C. Sampling distribution of statistics
- D. None of these
Explanation: The standard deviation of a statistic's sampling distribution measures its typical sampling-to-sampling variation and is called the…
Correct answer: Standard error of statistics- A. Sometimes normal for all sample sizes
- B. Sometimes normal for large sample sizes
- C. Always normal for all sample sizes
- D. Always normal for large sample sizes
Explanation: By the central limit theorem, the sampling distribution of the sample mean becomes approximately normal for large samples, regardless of…
Correct answer: Always normal for large sample sizes- A. Probabilistic sampling
- B. Stratified sampling
- C. No probabilistic sampling
- D. Cluster sampling
Explanation: Convenience sampling selects units because they are easy to reach rather than giving every unit a known chance of selection.
Correct answer: No probabilistic sampling- A. 4
- B. 8
- C. 16
- D. 32
Explanation: With replacement, each of the 2 selections has 4 possible outcomes, so the total number of ordered samples is 4 × 4 = 16.
Correct answer: 16- A. Increasing the sample size
- B. Decreasing the sample size
- C. Increasing population s.d.
- D. None of these
Explanation: A larger sample usually gives a more stable estimate and reduces sampling variability, with standard error decreasing roughly as the…
Correct answer: Increasing the sample size- A. Only once
- B. More than once
- C. Less than once
- D. None
Explanation: In sampling with replacement, a selected unit is returned to the population before the next draw.
Correct answer: More than once- A. Systematic
- B. Cluster
- C. Stratified
- D. Judgment
Explanation: Judgment sampling selects items based on the investigator's or purchaser's assessment rather than by a random mechanism.
Correct answer: Judgment- A. Biased sampling
- B. Non-prob.sampling
- C. Less than sampling
- D. Representative sampling
Explanation: Non-random sampling does not give every population unit a known or equal chance of selection, so it is commonly called non-probability…
Correct answer: Non-prob.sampling533. A sampling distribution is the probability distribution for which one of the following___________?
- A. A sample
- B. A sample statistic
- C. A population
- D. A population parameter
Explanation: A sampling distribution describes how a statistic, such as a sample mean or proportion, varies across all possible samples from a…
Correct answer: A sample statistic- A. Approximately normal because the sample size is small relative to the population size
- B. Approximately normal because of the central limit theorem
- C. Exactly
- D. None of these alternatives is correct
Explanation: With a sample size of only 17, the central limit theorem alone cannot ensure an approximately normal sample-mean distribution, because no…
Correct answer: None of these alternatives is correct- A. Bias
- B. Standard
- C. Sampling error
- D. both (a) and (b)
Explanation: Sampling error is the difference between a sample statistic and the corresponding population parameter.
Correct answer: Sampling error- A. Serious error
- B. Dispersion
- C. Standard error
- D. Difference
Explanation: The standard deviation of a statistic's sampling distribution is called its standard error.
Correct answer: Standard error- A. Unknown
- B. Large
- C. Small
- D. Know
Explanation: In probability sampling, every sampling unit has a known, nonzero probability of selection.
Correct answer: Know- A. Four
- B. Six
- C. Three
- D. Seven
Explanation: The four commonly taught probability sampling methods are simple random, stratified, systematic, and cluster sampling.
Correct answer: Four- A. Sampling frame
- B. Sampling units
- C. Sample pop
- D. Sample design
Explanation: A sampling unit is the smallest identifiable member or group of members selected in a sample, such as a person, household, or institution.
Correct answer: Sampling units- A. Only Once
- B. More than once
- C. Less than once
- D. None of these
Explanation: In sampling without replacement, a selected unit is removed from further consideration, so it cannot be selected again.
Correct answer: Only Once