Free Sampling and Sampling Distributions MCQs with Answers

32 Sampling and Sampling Distributions MCQs from Statistics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

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32 questions · page 2 of 4

11. E(x1 - x2)= ___________________?

Moderate
  • 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

12. The standard deviation of sampling distribution of a statistics is _________________?

Moderate
  • 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 standard error of that statistic. Sampling error is an individual difference, not the standard deviation itself.

Correct answer: Standard error of statistics

13. For a population with any distribution, the form of the sampling distribution of the sample mean is_____________?

Moderate
  • 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 the population's distribution. Option d is the intended answer, with “normal” understood as approximately normal.

Correct answer: Always normal for large sample sizes

14. Convenience sampling is an example of______________?

Moderate
  • 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. It is therefore a non-probability sampling method.

Correct answer: No probabilistic sampling

15. For a population consisting of 4 members, a sample of size '2' is taken replacement, then the number of all the possible samples are?

Moderate
  • 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. This gives option c.

Correct answer: 16

16. Sampling errors are reduced by:___________________?

Moderate
  • 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 inverse square root of sample size. Thus increasing the sample size is the appropriate choice.

Correct answer: Increasing the sample size

17. In sampling with replacement be t a sampling unit can selected________________?

Moderate
  • 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. Consequently, the same unit may be selected more than once.

Correct answer: More than once

18. To purchase the fruit, we use the _________ sampling?

Moderate
  • 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. Choosing fruit based on visible quality is a typical judgment-sampling situation.

Correct answer: Judgment

19. Non-random sampling is also called___________________?

Moderate
  • 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 sampling. It may also introduce selection bias, but option b is the standard name.

Correct answer: Non-prob.sampling

20. A sampling distribution is the probability distribution for which one of the following___________?

Moderate
  • 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 population. It is not the distribution of one particular sample or of the population parameter itself.

Correct answer: A sample statistic