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Chapter 6: Q3 (page 263)

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

Expert verified

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

01

Given information

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

02

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.

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