Estimators Evaluation

Calculate the bias of an estimator if the true value is 10 and the estimator gives an average value of 9.5 based on 5 samples.

• -0.5

• 2.5

• 1.5

• 0.5

Determine the variance of an estimator if the true value is 20 and the estimator gives values of 18, 22, 19, 21, and 20 based on 5 samples.

• 1.2

• 0.5

• 2.0

• 3.5

Explain what it means for an estimator to be consistent.

• The estimator is consistent if it converges in probability to the true value as the sample size increases.

• The estimator is consistent if it remains constant regardless of the sample size.

• The estimator is consistent if it diverges in probability to the true value as the sample size increases.

• The estimator is consistent if it converges in probability to the false value as the sample size increases.

Define efficiency in the context of estimators and provide an example.

• An example of efficiency in estimators is the use of the sample mean as an estimator for the population mean, which is known to be efficient under certain conditions.

• Using the smallest value in the sample as an estimator for the population mean

• Using the median as an estimator for the population mean

• Using the largest value in the sample as an estimator for the population mean

Apply the concept of unbiased estimators to calculate the mean of a sample with values 8, 10, 12, 9, and 11.

• 13

• 10

• 11

• 8

Compare the bias and variance of two different estimators and discuss which one is preferable.

• Estimator with low bias and high variance

• Estimator with high bias and low variance

• Estimator with high bias and high variance

• Estimator with low bias and low variance

Calculate the bias of an estimator if the true value is 30 and the estimator gives an average value of 28 based on 10 samples.

• 5

• 20

• -2

• 12

Determine the variance of an estimator if the true value is 15 and the estimator gives values of 14, 16, 15, 17, and 15 based on 10 samples.

• 2.5

• 0.8

• 1.2

• 3.0

Explain the concept of consistency in the context of estimators and provide an example.

• An example of consistency in estimators is the sample mean, which consistently converges to the population mean as the sample size increases.

• An example of consistency in estimators is the sample mean, which consistently converges to the population mean as the sample size decreases.

• An example of consistency in estimators is the median, which consistently converges to the population mean as the sample size increases.

• Consistency in estimators means that the estimate remains the same regardless of the sample size.

Define efficiency in the context of estimators and discuss why it is important in statistical analysis.

• Efficiency is the ability of an estimator to provide estimates with high variability using the available data.

• Efficiency is not important in statistical analysis.

• Efficiency is the ability of an estimator to provide imprecise and inaccurate estimates using the available data.

• Efficiency is the ability of an estimator to provide precise and accurate estimates using the available data.