The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 146414253X
ISBN 13: 978-1-46414-253-6

Chapter 19 - From Data Production to Inference: Part III Review - Supplementary Exercises - Page 452: 19.64

Answer

See below.

Work Step by Step

Power refers to the probability of rejecting the null hypothesis in case of the alternative hypothesis being true. Thus a test with a low power has a low probability of rejecting the null hypothesis even when it should be rejected. Thus in case of a test with low power where the null hypothesis isn't rejected, it is still quite likely that the null hypothesis isn't true.
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