Point Estimation

Description: This quiz covers the fundamental concepts and methods related to point estimation in statistics. It aims to assess your understanding of various estimators, their properties, and their applications in statistical inference.
Number of Questions: 15
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Tags: point estimation estimators sampling distributions confidence intervals hypothesis testing
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In point estimation, what is the primary objective?

  1. To find the exact value of the population parameter

  2. To obtain an estimate of the population parameter based on sample data

  3. To determine the probability distribution of the population parameter

  4. To test the hypothesis about the population parameter


Correct Option: B
Explanation:

The primary objective of point estimation is to use sample data to obtain an estimate of the unknown population parameter, rather than finding its exact value or testing hypotheses about it.

Which of the following is an example of a point estimator?

  1. Sample mean

  2. Population mean

  3. Standard deviation

  4. Hypothesis test statistic


Correct Option: A
Explanation:

The sample mean is a point estimator for the population mean. It is calculated by summing the values in a sample and dividing by the sample size.

What is the sampling distribution of a point estimator?

  1. The distribution of the estimator in repeated samples of the same size

  2. The distribution of the population parameter in repeated samples of the same size

  3. The distribution of the sample data in repeated samples of the same size

  4. The distribution of the hypothesis test statistic in repeated samples of the same size


Correct Option: A
Explanation:

The sampling distribution of a point estimator describes the distribution of the estimator in repeated samples of the same size. It provides information about the estimator's variability and its accuracy.

Which property of a point estimator ensures that its expected value is equal to the population parameter?

  1. Unbiasedness

  2. Consistency

  3. Efficiency

  4. Sufficiency


Correct Option: A
Explanation:

Unbiasedness is the property of a point estimator that ensures that its expected value is equal to the population parameter. This means that, on average, the estimator will produce estimates that are close to the true value of the parameter.

What is the purpose of a confidence interval in point estimation?

  1. To provide an estimate of the population parameter

  2. To determine the probability distribution of the population parameter

  3. To test the hypothesis about the population parameter

  4. To provide a range of plausible values for the population parameter


Correct Option: D
Explanation:

A confidence interval provides a range of plausible values for the population parameter based on sample data. It is constructed using the point estimator and the sampling distribution of the estimator.

Which of the following factors affects the width of a confidence interval?

  1. Sample size

  2. Level of confidence

  3. Variability of the population

  4. All of the above


Correct Option: D
Explanation:

The width of a confidence interval is affected by the sample size, the level of confidence, and the variability of the population. A larger sample size, a higher level of confidence, and a more variable population will all lead to a wider confidence interval.

What is the relationship between point estimation and hypothesis testing?

  1. Point estimation is a necessary step before hypothesis testing

  2. Hypothesis testing is a necessary step before point estimation

  3. Point estimation and hypothesis testing are independent procedures

  4. Point estimation and hypothesis testing are always used together


Correct Option: A
Explanation:

In general, point estimation is a necessary step before hypothesis testing. This is because the point estimate provides an initial estimate of the population parameter, which is then used to formulate and test the hypothesis.

Which of the following is an example of a consistent estimator?

  1. Sample mean

  2. Sample median

  3. Sample proportion

  4. All of the above


Correct Option: D
Explanation:

All of the given estimators (sample mean, sample median, and sample proportion) are consistent estimators. This means that as the sample size increases, the estimates obtained from these estimators will converge to the true value of the population parameter.

What is the efficiency of an estimator?

  1. The ratio of the variance of the estimator to the variance of the population parameter

  2. The ratio of the variance of the estimator to the variance of the sampling distribution

  3. The ratio of the variance of the population parameter to the variance of the estimator

  4. The ratio of the variance of the sampling distribution to the variance of the estimator


Correct Option: A
Explanation:

The efficiency of an estimator is measured by the ratio of the variance of the estimator to the variance of the population parameter. A more efficient estimator will have a smaller variance and will produce estimates that are closer to the true value of the parameter.

What is the concept of sufficiency in point estimation?

  1. A sufficient statistic contains all the information about the population parameter

  2. A sufficient statistic is independent of the sample size

  3. A sufficient statistic is unbiased

  4. A sufficient statistic is efficient


Correct Option: A
Explanation:

A sufficient statistic is a statistic that contains all the information about the population parameter that is contained in the entire sample. This means that, given a sufficient statistic, no additional information can be obtained from the sample regarding the population parameter.

Which of the following is an example of a sufficient statistic for the mean of a normal distribution?

  1. Sample mean

  2. Sample median

  3. Sample variance

  4. Sample standard deviation


Correct Option: A
Explanation:

The sample mean is a sufficient statistic for the mean of a normal distribution. This means that, given the sample mean, no additional information can be obtained from the sample regarding the mean of the population.

What is the Neyman-Pearson lemma in point estimation?

  1. It provides a method for constructing uniformly most powerful tests

  2. It provides a method for constructing unbiased estimators

  3. It provides a method for constructing efficient estimators

  4. It provides a method for constructing sufficient statistics


Correct Option: A
Explanation:

The Neyman-Pearson lemma provides a method for constructing uniformly most powerful tests of hypotheses. It is a fundamental result in statistical inference and is used to derive optimal tests for various statistical problems.

Which of the following is an example of a maximum likelihood estimator?

  1. Sample mean

  2. Sample median

  3. Sample proportion

  4. All of the above


Correct Option: C
Explanation:

The sample proportion is an example of a maximum likelihood estimator. It is the value of the population proportion that maximizes the likelihood function of the sample data.

What is the method of moments in point estimation?

  1. A method for constructing unbiased estimators

  2. A method for constructing consistent estimators

  3. A method for constructing efficient estimators

  4. A method for constructing sufficient statistics


Correct Option: A
Explanation:

The method of moments is a method for constructing unbiased estimators. It involves equating the sample moments to the corresponding population moments and solving for the unknown population parameters.

Which of the following is an example of a Bayesian estimator?

  1. Sample mean

  2. Sample median

  3. Sample proportion

  4. Posterior mean


Correct Option: D
Explanation:

The posterior mean is an example of a Bayesian estimator. It is the expected value of the population parameter given the observed sample data and prior information.

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