Quiz: QZ-20260908-88427

Quiz Details

QZ-20260908-88427

Topics:

Point estimation Sufficient statistics Minimal sufficient statistics Maximum likehood estimators Evaluating estimators

Difficulty: Level 3 - Medium

Questions: 13

Language: English (English)

Generated: September 08, 2026 at 10:17 AM

Generated by: NANZIRI PATIENCE

Instructions: Select an answer for each question and click "Check Answer" to see if you're correct. Then view the explanation to learn more!

1 What is a point estimator?

A) A theoretical value that cannot be calculated.

B) A measure of variability in a sample.

C) A range of values that estimates a population parameter.

D) A statistic that provides a single value estimate of a population parameter.

Correct Answer: D
Explanation: A point estimator gives a single best guess or estimate of an unknown population parameter.

2 Which of the following is a property of sufficient statistics?

A) It is always the sample mean.

B) It captures all the information needed about the parameter from the sample.

C) It cannot be derived from the likelihood function.

D) It is unique for every distribution.

Correct Answer: B
Explanation: A sufficient statistic retains all the information needed to estimate the parameter based on the sample data.

3 What distinguishes minimal sufficient statistics from other sufficient statistics?

A) It cannot be derived from a larger sufficient statistic.

B) It contains no redundant information.

C) It is the simplest form of sufficient statistic.

D) All of the above.

Correct Answer: D
Explanation: Minimal sufficient statistics are indeed the simplest and contain no redundant information while still being sufficient.

4 Which method is commonly used to find maximum likelihood estimators?

A) Minimizing the variance.

B) Applying Bayesian methods.

C) Maximizing the likelihood function.

D) Calculating the mean.

Correct Answer: C
Explanation: Maximum likelihood estimators are found by maximizing the likelihood function with respect to the parameters.

5 Which of the following is a characteristic of a good estimator?

A) It should always yield the same value.

B) It should be consistent.

C) It should only work with large samples.

D) It should be biased.

Correct Answer: B
Explanation: Consistency is a key property of a good estimator, meaning that as the sample size increases, the estimators converge in probability to the true parameter value.

6 In the context of point estimation, what does bias refer to?

A) The range of values an estimator can take.

B) The variability of the estimator across samples.

C) The accuracy of the data collection method.

D) The difference between the expected value of the estimator and the true parameter.

Correct Answer: D
Explanation: Bias is defined as the difference between an estimator's expected value and the true value of the parameter being estimated.

7 The Rao-Blackwell theorem is useful for finding which of the following?

A) A better estimator from a given one.

B) A non-parametric estimator.

C) A biased estimator.

D) A sufficient statistic.

Correct Answer: A
Explanation: The Rao-Blackwell theorem states that one can improve an estimator by conditioning on a sufficient statistic.

8 What is the primary goal of evaluating an estimator?

A) To assess its efficiency and consistency.

B) To calculate its mean.

C) To find the sample size needed.

D) To determine if it is unbiased.

Correct Answer: A
Explanation: Evaluating an estimator involves assessing its efficiency, bias, and consistency to determine its reliability in estimating parameters.

9 Which of the following is NOT a common criterion for evaluating estimators?

A) Consistency.

B) Bias.

C) Efficiency.

D) Sufficiency.

Correct Answer: D
Explanation: Sufficiency is a property related to the information captured by a statistic rather than a criterion for evaluating an estimator.

10 What does the term 'asymptotic normality' refer to in statistics?

A) An estimator is always normally distributed.

B) An estimator only works for normal populations.

C) An estimator's distribution approaches a normal distribution as sample size increases.

D) An estimator becomes biased as sample size increases.

Correct Answer: C
Explanation: Asymptotic normality means that as the sample size increases, the distribution of the estimator approaches a normal distribution under certain conditions.

11 Which of the following statements about maximum likelihood estimation (MLE) is true?

A) MLE is always unbiased.

B) MLE can be used for any type of data.

C) MLE is always less efficient than other methods.

D) MLE may not exist for all models.

Correct Answer: D
Explanation: While MLE is a powerful method, there are cases where the maximum likelihood estimators do not exist for certain models or parameter spaces.

12 Which of the following statements is true regarding the efficiency of an estimator?

A) Efficiency can be measured only in large samples.

B) Efficiency is unrelated to sample size.

C) More efficient estimators have a smaller variance.

D) All efficient estimators are unbiased.

Correct Answer: C
Explanation: An efficient estimator has the smallest variance among the class of unbiased estimators for a given sample size.

13 What is the role of the likelihood function in statistics?

A) To provide a measure of the sample mean.

B) To estimate the sample size required for analysis.

C) To quantify how likely a given parameter is given the observed data.

D) To determine the variance of the sample.

Correct Answer: C
Explanation: The likelihood function helps to quantify the probability of observing the given data under various parameter values, playing a central role in maximum likelihood estimation.

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