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9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 8.2, Problem 27E

Textbook Problem

Show that for any Δ > 0, when the population distribution is normal and *σ* is known, the two-tailed test satisfies *β*(*μ*_{0} − Δ) = *β*(*μ*_{0} + Δ), so that *β*(*μ*′) is symmetric about *μ*_{0}.

Expert Solution

To determine

Show that for two tailed test,

**Given info:**

The population distribution is normal and the population standard deviation is known. The additional information is that if

**Calculation:**

From the definition of

Where

It is known that

Assuming *z*,

And assuming *z,*

Probability and Statistics for Engineering and the Sciences

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