hree different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration. Three overlapping bell shaped curves are all plotted above the same horizontal axis. The three curves are labeled "Statistic I," "Statistic II," and "Statistic III." Statistic II and III are both centered at a point on the axis labeled "True value of population characteristic." The shape of Statistic II is narrower and taller than the other curves. Statistic I and III have a similar shape, but Statistic I is centered to the right of where Statistic II and III are centered. Which statistic would you recommend? (Hint: See the section on choosing a statistic.) Statistic I Statistic II Statistic III Explain your choice. This statistic is biased, but it has a much lower standard deviation than the other two. This statistic is biased, but it has a much higher standard deviation than the other two. The standard deviation of this statistic isn't the highest, but it is the only unbiased statistic out of the three. The standard deviation of this statistic isn't the lowest, but it is the only unbiased statistic out of the three. This statistic is unbiased and has the smallest standard deviation of the three. This statistic is unbiased and has the largest standard deviation of the three.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 11MCQ

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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.

Three overlapping bell shaped curves are all plotted above the same horizontal axis. The three curves are labeled "Statistic I," "Statistic II," and "Statistic III."

Statistic II and III are both centered at a point on the axis labeled "True value of population characteristic."
The shape of Statistic II is narrower and taller than the other curves.
Statistic I and III have a similar shape, but Statistic I is centered to the right of where Statistic II and III are centered.

Which statistic would you recommend? (Hint: See the section on choosing a statistic.)

Statistic I

Statistic II

Statistic III

Explain your choice.

This statistic is biased, but it has a much lower standard deviation than the other two.

This statistic is biased, but it has a much higher standard deviation than the other two.

The standard deviation of this statistic isn't the highest, but it is the only unbiased statistic out of the three.

The standard deviation of this statistic isn't the lowest, but it is the only unbiased statistic out of the three.

This statistic is unbiased and has the smallest standard deviation of the three.

This statistic is unbiased and has the largest standard deviation of the three.