Introductory Statistics 9th Edition

Published by Wiley
ISBN 10: 1-11905-571-7
ISBN 13: 978-1-11905-571-6

Chapter 7 - Section 7.2 - Mean and Standard Deviation of x - Exercises - Page 283: 7.9

Answer

If an estimator is consistent, the standard deviation of $\bar{x}\ $ should decrease when the sample size increases. The estimator, $\bar{x}\ $ will be a consistent estimator. This is because by the formula, when the n is increased, the value of the standard deviation will be reduced.

Work Step by Step

If an estimator is consistent, the standard deviation of $\bar{x}\ $ should decrease when the sample size increases. The estimator, $\bar{x}\ $ will be a consistent estimator. This is because by the formula, when the n is increased, the value of the standard deviation will be reduced.
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