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Hypothesis tests for μ, p-values for t-tests
Hypothesis tests for μ, p-values for t-tests

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School
Colorado State University
Department
Statistics
Course
STAT 301
Professor
Brett Hunter
Semester
Fall

Description
7 October Hypothesis Tests for μ 2 cases σ known – rarely happens σ unknown σ known Test statistic x−μ 0 σ Z test ~ N(0,1) √n Assuming that n ≥ 30 (or X has a normal distribution i.e., normal population distribution) p-value If HA: μ > μ0, then p-value = P(Z > Z )test If HA: μ < μ0, then p-value = P(Z < Z )test ≠ If HA: μ μ0, then p-value = P(Z > |Z |test σ unknown Assumption is still n ≥ 30 (or X~Normal) Test statistic x−μ 0 s ttest ~ tn-1 √n Follows t-distribution with n – 1 degrees of freedom p-value If HA: μ > μ0, then p-value = P(t n-1> ttest If HA: μ < μ0, then p-value = P(t n-1 )test ≠ If HA: μ μ 0 then p-value = 2 P(t n-1 > |test How to find P(t > t )?test Use Table 4 Recall that the t-distribution is symmetric and based on some degrees of freedom Using Table 4 Table gives probabilities where P(t > t ) can
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