Free Estimation MCQs with Answers
21 Estimation 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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- A. Shorter
- B. Wider
- C. Large
- D. Small
Explanation: For a fixed confidence level, a shorter confidence interval is preferred because it gives a more precise estimate of the population…
Correct answer: Shorter- A. Accuracy
- B. Precision
- C. Error
- D. All of above
Explanation: A confidence interval expresses the precision of an estimate by showing a range of plausible parameter values.
Correct answer: Precision- A. Estimate
- B. Test Statistics
- C. Estimation
- D. Sample
- E. Estimator
Explanation: An estimate is the numerical quantity produced after an estimator, such as a formula or rule, is applied to sample data.
Correct answer: Estimate- A. Constant
- B. Variable
- C. All of above
- D. Non of these
Explanation: A parameter describes a population and has one fixed value, even though that value is usually unknown.
Correct answer: Constant- A. 652 and . 728
- B. .314 and .652
- C. .798 and .745
- D. None of these
Explanation: For a proportion, the 90% interval is p ± 1.645√[p(1−p)/n]. Substituting p = .69 and n = 400 gives approximately .69 ± .038, or .652 to…
Correct answer: 652 and . 728- A. x±1.65 6/√n
- B. u±1.95 S/√n
- C. x±1.96 6/√n
- D. ±1.96 6/√n
Explanation: For a 95% large-sample confidence interval for μ, use x̄ ± 1.96σ/√n. The value 1.65 corresponds approximately to a 90% two-sided interval…
Correct answer: x±1.96 6/√n- A. C.I.
- B. Point estimator
- C. Parameter
- D. Point estimate
Explanation: A point estimate reports an estimated parameter as one numerical value, such as x̄ = 40.
Correct answer: Point estimate- A. (U)
- B. 6
- C. Ux
- D. 6/√n
Explanation: If x̄ = 40 is used to estimate the population mean, its target is μ. The symbols in the other choices refer to different parameters or to…
Correct answer: (U)- A. Biased
- B. Parameter
- C. Unbiased
- D. None of these
Explanation: For a random sample, the sample proportion p̂ has expected value equal to the population proportion P, so it is unbiased.
Correct answer: Unbiased- A. Unbiased
- B. Consistent
- C. Sufficient
- D. Efficient
Explanation: An estimator is unbiased when its expected value equals the parameter it estimates, so E(θ̂)=θ is the defining condition.
Correct answer: Unbiased- A. Unbiased
- B. Sufficient
- C. Consistent
- D. Efficient
Explanation: By the conditional-distribution characterization of sufficiency, S is sufficient for θ when the distribution of the sample given S=s does…
Correct answer: Sufficient- A. It is a function of some other set of sufficient statistics.
- B. It is a function of every other set of sufficient
- C. It is a function of any sufficient statistics in the set.
- D. It is not a function of every other set of sufficient statistics.
Explanation: A minimal sufficient statistic contains the least information needed for sufficiency and can be expressed as a function of every other…
Correct answer: It is a function of every other set of sufficient- A. MSE(θˆ)=SD(θˆ)+Bias
- B. MSE(θˆ)=Var(θˆ)+Bias2
- C. MSE(θˆ)=SD(θˆ)+Bias2
- D. MSE(θˆ)=Var(θˆ)+Bias
Explanation: The mean squared error decomposes into variance plus squared bias: MSE(θ̂)=Var(θ̂)+[Bias(θ̂)]².
Correct answer: MSE(θˆ)=Var(θˆ)+Bias2- A. Standard Deviation
- B. Mean
- C. mean Square Error
- D. Variance
Explanation: Consistency is commonly examined through the estimator's variance as the sample size increases: a consistent estimator should have…
Correct answer: Variance- A. Consistency
- B. All Above
- C. Unbiasedness
- D. Efficiency
Explanation: A good point estimator is judged by several properties, especially unbiasedness, consistency, and efficiency.
Correct answer: All Above- A. P±2.18√p2q2/n
- B. P±1.65(pq/n)
- C. P±1.96 p2q2/√n
- D. P±1.96√p2q2/n
Explanation: For a population proportion, the 95% confidence interval is estimated proportion ± 1.96√(pq/n), where q = 1 − p.
Correct answer: P±1.96√p2q2/n- A. Sampling
- B. Probability distribution
- C. Regression
- D. Statistical Inference
Explanation: Statistical inference uses sample information to draw conclusions about a population.
Correct answer: Statistical Inference- A. Estimate
- B. Estimator
- C. Probability
- D. Numerical
Explanation: An estimate is the numerical value obtained from a sample statistic for estimating a population parameter.
Correct answer: Estimate- A. Q
- B. X
- C. Ux
- D. u
Explanation: A sample mean is unbiased for the population mean when its expected value equals that population mean, written E(X̄) = μX.
Correct answer: u- A. the methods to make decisions about population based on sample results
- B. how to make decisions about mean, median, or mode
- C. how a sample is obtained from a population
- D. None of the above
Explanation: Inferential statistics uses sample results to draw conclusions or make decisions about the wider population.
Correct answer: the methods to make decisions about population based on sample resultsEstimation MCQs: common questions
Are these Estimation MCQs free?
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There are 21 Estimation MCQs in the Statistics bank, shown 20 to a page with the correct answer and an explanation on each.
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