Page 569 - Probability and Statistical Inference

546 12. Large-Sample Inference

Two-Sided Alternative Hypothesis
Here we test H : µ = µ versus H : µ ≠ µ . Along the lines of Section
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11.2.1, we can propose the following two-sided approximate level α test:

Figure 12.3.4. Two-Sided Standard Normal Rejection Region
Next, let us briefly address the two-sample problems. With preassigned α
∈ (0, 1), we wish to test a null hypothesis H : µ = µ with an approximate
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level α. The specific alternative hypotheses will be given shortly. Using (12.3.5),
one considers the test statistic

for large n , n when µ = µ .
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Upper-Sided Alternative Hypothesis
Here we test H : µ = µ versus H : µ > µ . See, for example, the Figure
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12.3.2. Along the lines of Section 8.4, we can propose the following upper-
sided approximate level α test:
Lower-Sided Alternative Hypothesis
Here we test H : µ = µ versus H : µ < µ . See, for example, the Figure
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12.3.3. Along the lines of Section 8.4, we can propose the following lower-
sided approximate level α test: