Question

Critical Thinking Challenges The power of a test (1 - ?) can be calculated when a specific value of the mean is hypothesized in the alternative hypothesis; for example, let $H_0: \mu = 50$ and let $H_1: \mu = 52$. To find the power of a test, it is necessary to find the value of ?. This can be done by the following steps: Step 1 For a specific value of ? find the corresponding value of X, using $z = \frac{X - \mu}{\sigma/\sqrt{n}}$ where ? is the hypothesized value given in $H_0$. Use a right-tailed test. Step 2 Using the value of X found in step 1 and the value of ? in the alternative hypothesis, find the area corresponding to z in the formula $z = \frac{X - \mu}{\sigma/\sqrt{n}}$ Step 3 Subtract this area from 0.5000. This is the value of ?. Step 4 Subtract the value of ? from 1. This will give you the power of a test. See Figure 8-41. 8-72 1. Find the power of a test, using the hypotheses given previously and ? = 0.05, ? = 3, and n = 30. FIGURE 8-41 Relationship Among ?, ?, and the Power of a Test Answers to Applying the Concepts 485 2. Select several other values for ? in $H_1$ and compute the power of the test. Generalize the results.

          Critical Thinking Challenges
The power of a test (1 - ?) can be calculated when a
specific value of the mean is hypothesized in the alternative
hypothesis; for example, let $H_0: \mu = 50$ and let $H_1: \mu = 52$.
To find the power of a test, it is necessary to find the value
of ?. This can be done by the following steps:
Step 1 For a specific value of ? find the corresponding
value of X, using $z = \frac{X - \mu}{\sigma/\sqrt{n}}$ where ? is the
hypothesized value given in $H_0$. Use a right-tailed
test.
Step 2 Using the value of X found in step 1 and the
value of ? in the alternative hypothesis,
find the area corresponding to z in the
formula $z = \frac{X - \mu}{\sigma/\sqrt{n}}$
Step 3 Subtract this area from 0.5000. This is the value
of ?.
Step 4 Subtract the value of ? from 1. This will give you
the power of a test. See Figure 8-41.
8-72
1. Find the power of a test, using the hypotheses
given previously and ? = 0.05, ? = 3, and
n = 30.
FIGURE 8-41
Relationship Among ?, ?,
and the Power of a Test
Answers to Applying the Concepts 485
2. Select several other values for ? in $H_1$ and
compute the power of the test. Generalize the
results.

Critical Thinking Challenges
The power of a test (1 - ?) can be calculated when a
specific value of the mean is hypothesized in the alternative
hypothesis; for example, let H0: μ = 50 and let H1: μ = 52.
To find the power of a test, it is necessary to find the value
of ?. This can be done by the following steps:
Step 1 For a specific value of ? find the corresponding
value of X, using z = (X - μ)/(σ/√(n)) where ? is the
hypothesized value given in H0. Use a right-tailed
test.
Step 2 Using the value of X found in step 1 and the
value of ? in the alternative hypothesis,
find the area corresponding to z in the
formula z = (X - μ)/(σ/√(n))
Step 3 Subtract this area from 0.5000. This is the value
of ?.
Step 4 Subtract the value of ? from 1. This will give you
the power of a test. See Figure 8-41.
8-72
1. Find the power of a test, using the hypotheses
given previously and ? = 0.05, ? = 3, and
n = 30.
FIGURE 8-41
Relationship Among ?, ?,
and the Power of a Test
Answers to Applying the Concepts 485
2. Select several other values for ? in H1 and
compute the power of the test. Generalize the
results.

Added by Alexander D.

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