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Hypothesis tests for a mean

Use a p-value · Diagrams · Complete reading

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Observed tail probabilities

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Three normal curves show observed tails beyond −2, beyond 2, and beyond both −2 and 2. One-sided probability is 0.0228; the two-sided total is 0.0455.
Three normal curves show observed tails beyond −2, beyond 2, and beyond both −2 and 2. One-sided probability is 0.0228; the two-sided total is 0.0455.
Three normal curves show observed tails beyond −2, beyond 2, and beyond both −2 and 2. One-sided probability is 0.0228; the two-sided total is 0.0455.
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Compare p-values and critical values at 5%

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For observations −1.5 and 1.5, the one-sided p-value 0.0668 exceeds 0.05, so do not reject. For two-sided z=2, p=0.0455 and |z|>1.960, so reject. Darker shading marks the probability beyond the observation.
For observations −1.5 and 1.5, the one-sided p-value 0.0668 exceeds 0.05, so do not reject. For two-sided z=2, p=0.0455 and |z|>1.960, so reject. Darker shading marks the probability beyond the observation.
For observations −1.5 and 1.5, the one-sided p-value 0.0668 exceeds 0.05, so do not reject. For two-sided z=2, p=0.0455 and |z|>1.960, so reject. Darker shading marks the probability beyond the observation.
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