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Unformatted text preview: set. • calculate a test statistic for hypothesis testing. • calculate a p‐value for the test. For a chosen significance level α , the decision rule is to reject the null hypothesis if: p‐value < α This rule gives the same conclusion as presented above. That is, when p‐value < α the calculated test statistic must be in the rejection region for the test. 11 Chapter 10 Chapter 10.3 Hypothesis Tests of the Mean Continued The discussion has considered testing the null hypothesis: H0 : μ ≤ a or H0 : μ = a against the one‐sided alternative hypothesis: H1 : μ > a The proposal for the test statistic was: z= x−a σ n In applied work, replace the unknown population parameter σ with the sample standard deviation s to get the t‐test statistic: t= x−a s n For a significance level α , the decision rule is to reject the null hypothesis H0 if: t > tc where t c is the critical value that satisfies: P(t ( n − 1 ) > t c ) = α t ( n − 1 ) is a random variable that has a t‐distribution with (n – 1) degrees of freedom. The critical value can be found from the Appendix Table for the t‐distribution. 12 Chapter 10 The calculation of a p‐value for the test is demonstrated in the grap...
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