2. Statistical Methods

Estimation Theory — Quiz

Test your understanding of estimation theory with 5 practice questions.

Practice Questions

Question 1

Which of the following statements correctly defines the mean squared error (MSE) of an estimator $\hat{\theta}$ for a parameter $\theta$?

Question 2

An estimator $\hat{\theta}$ for a parameter $\theta$ is considered unbiased if which of the following conditions holds true?

Question 3

Which of the following properties of an estimator indicates that it achieves the lowest possible variance among all unbiased estimators?

Question 4

When constructing a confidence interval for a population mean, if the population standard deviation ($\sigma$) is unknown and the sample size ($n$) is small (typically $n < 30$), which distribution is most appropriate to use for calculating the critical value?

Question 5

An actuary is estimating the average claim amount for a new insurance product. They collect a sample of claim amounts and calculate a 90% confidence interval. If they want to decrease the width of the confidence interval while keeping the confidence level at 90%, which of the following actions would be most effective?