sta 2006 0809_lecturenotes_6

# sta 2006 0809_lecturenotes_6 - Hypotheses Testing Concepts...

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Hypotheses Testing Concepts 1. null hypothesis 2. alternative hypothesis (a) one-sided (b) two-sided 3. type I error 4. type II error 5. signiﬁcance level of a test 6. power of a test 7. test statistics 8. critical region 9. p -value 65

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A. Test about a normal mean 1. σ 2 known 2. σ 2 unknown 3. Large sample size (Normal data?) 66
Example Let X (in millimeters) equal the growth in 15 days of a tumor induced in a mouse. Assume that the distribution of X is N ( μ,σ 2 ). We shall test the null hypothesis H 0 : μ = 4 . 0 millimeters against the two-sided alternative hypothesis H 1 : μ 6 = 4 . 0 Let the sample size n = 9 and the sample mean and standard de- viation are 4.3 and 1.2 respectively. Test the null hypothesis with a signiﬁcance level of α = 0 . 1 Compute the p -value. 67

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Example Let X (in millimeters) equal the growth in 15 days of a tumor induced in a mouse. Assume that the distribution of X is N ( μ,σ 2 ). We shall test the null hypothesis H 0 : μ = 4 . 0 millimeters against the one-sided alternative hypothesis
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sta 2006 0809_lecturenotes_6 - Hypotheses Testing Concepts...

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