All Free Statistics MCQs with Answers
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545 questions · page 53 of 55
521. Which sampling method we will apply if there is no sampling frame?
- 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 identified. The clusters then serve as the practical sampling units.
Correct answer: Cluster sampling522. Cluster sampling is useful when sampling units are__________?
- 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 fieldwork costs. The wording means the units are spread over a wide area.
Correct answer: Far a part523. condition for applying Central Limit Theorem (CLT) which approximate the sampling distribution of the mean with a normal distribution is ?
- 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 population is not strongly nonnormal. The exact requirement depends on the population shape, but option a is the intended guideline.
Correct answer: n > 30524. E(x1 - x2)= ___________________?
- 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 - u2525. The standard deviation of sampling distribution of a statistics is _________________?
- 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 statistics526. For a population with any distribution, the form of the sampling distribution of the sample mean is_____________?
- 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 sizes527. Convenience sampling is an example of______________?
- 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 sampling528. For a population consisting of 4 members, a sample of size '2' is taken replacement, then the number of all the possible samples are?
- 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: 16529. Sampling errors are reduced by:___________________?
- 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 size530. In sampling with replacement be t a sampling unit can selected________________?
- 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