Question

Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which of these statistics are unbiased estimators of the population characteristic?

Name: Problem 2, Chapter 9: Statistics Learning From Data
Uploaded: 2022-04-06T19:14:11-08:00
Duration: 1 min 43 s
Channel: Varsha Aggarwal
Description: Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which of these statistics are unbiased estimators of the population characteristic?

   Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration:
Which of these statistics are unbiased estimators of the population characteristic?

Statistics Learning From Data

Thomas H. Short,… 2nd Edition

Chapter 9, Problem 2

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Solved by Expert Varsha Aggarwal

04/06/2022

Step 1

An estimator is considered unbiased if the expected value of the sampling distribution of the estimator is equal to the true value of the parameter being estimated. Mathematically, an estimator \(\hat{\theta}\) is unbiased for a parameter \(\theta\) if Show more…

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Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which of these statistics are unbiased estimators of the population characteristic?

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Key Concepts

Unbiased Estimator

An unbiased estimator is a statistic whose expected value, or mean of its sampling distribution, is equal to the true value of the population parameter it is estimating. This means that on average the estimator neither overestimates nor underestimates the parameter.

Expected Value

The expected value is the theoretical mean of a probability distribution, calculated as a weighted average of all possible values. In the context of estimators, it indicates the center of the sampling distribution and is used to determine whether an estimator is unbiased.

Sampling Distribution

A sampling distribution is the probability distribution of a given statistic based on a random sample. It shows the variability of the statistic from sample to sample and is central to making inferences about the population based on sample data.

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