Question

Unbiased Estimators Data Set 4 “Births” in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median; sample range; sample variance; sample standard deviation; sample proportion?

Short answer

Out of the given statistics, the sample mean, the sample variance, and the sample proportion are unbiased estimators of the corresponding population parameters.

Step-by-step solution

Given information

A sample of 400 birth weights is selected, and the sample statistics are computed.

Unbiased estimators

An unbiased estimator is a sample statistic when the sampling distribution of the statistic has a mean value equal to the corresponding population parameter.

It is known that the following statistics are unbiased estimators of their corresponding population parameters:

• Sample proportion
• Sample mean
• Sample variance

In addition, the following statistics are biased estimators of their population parameters:

• Sample median
• Sample range
• Sample standard deviation

Therefore, out of the given statistics, the sample mean, the sample variance, and the sample proportion are unbiased estimators of the corresponding population parameters.