Only need to compute p value once for any Fail to reject at the significance

# Only need to compute p value once for any fail to

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– Only need to compute p-value once for any 𝛼𝛼 Fail to reject 𝐻𝐻 0 at the significance level 𝛼𝛼 for any 𝛼𝛼 ≤ p - Value – Reject 𝐻𝐻 0 at the any significance level 𝛼𝛼 when 𝛼𝛼 > p-Value p-Value approach: tells how strongly (confidence that) we reject the null 𝐻𝐻 0 42
0 0 𝑧𝑧 43
Steps for Calculating the p-Value for a Test of Hypothesis1.Determine the value of the test statistic based on sampling data z 44
Steps for Calculating the p -Value for a Test of Hypothesis 2. If the test is one-tailed, the p -value is equal to the tail area beyond z in the same direction as the alternative hypothesis. 𝐻𝐻 𝑎𝑎 : 𝜇𝜇 < 𝜇𝜇 0 , the p-value is the area to the left of, or below, the observed z -value. 𝐻𝐻 𝑎𝑎 : 𝜇𝜇 > 𝜇𝜇 0 , the p −value is the area to the right of, or above, the observed z −value. 45
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𝑝𝑝 -value exercise Suppose your perform a test of the null hypothesis 𝐻𝐻 0 : 𝜇𝜇 =5 against the alternative 𝐻𝐻 𝑎𝑎 : 𝜇𝜇 <5. You observe a 𝑝𝑝 − value of 𝑝𝑝 =0.07. True, false, or not enough information: A level 5% test would reject 𝐻𝐻 0 A level 10% test would reject 𝐻𝐻 0 . 47
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Two-tailed test: 𝛼𝛼 = 0.05 Reject null when | 𝑧𝑧 | > | 𝑧𝑧 𝛼𝛼 / 2 | p-value < 𝛼𝛼 𝑧𝑧 0 Reject H 0 Reject H 0 1/2 p -value 1/2 p -value 𝜶𝜶 𝟐𝟐 = .025 𝜶𝜶 𝟐𝟐 = .025 𝑧𝑧 𝛼𝛼 / 2 −𝑧𝑧 𝛼𝛼 / 2 Equivalence between p-value & rejection region −𝑧𝑧 49
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