STAT
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# Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Stat 312: Lecture 15 P -values Moo K. Chung [email protected] November 2, 2004 1. The P -value is the smallest level of significance at which H 0 would be rejected. Example 8.5, 8.15. Nicotine contents X 1 , · · · X 32 of cigarettes follow N ( μ, 0 . 2 2 ). We are interested in testing if H 0 : μ = 1 . 5 vs. H 1 : μ > 1 . 5 . Assume ¯ x = 1 . 57. Given α level, the corre- sponding rejection regions are given by > -qnorm(0.05) [1] 1.644854 > -qnorm(0.025) [1] 1.959964 > -qnorm(0.01) [1] 2.326348 > -qnorm(0.005) [1] 2.575829 > (1.57-1.5)/(0.2/sqrt(32)) [1] 1.979899 > 1-pnorm(1.979899) [1] 0.02385744 2. P -value α reject H 0 at level α . P -value > α do not reject H 0 at level α . The smaller the P -value, the easier to reject
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Unformatted text preview: H . Example. Dog IQ example. > t.test(x,mu=100,alternative="less", conf.level=0.95) One Sample t-test data: x t = -4.2036, df = 9, p-value = 0.001147 alternative hypothesis: true mean is less than 100 95 percent confidence interval:-Inf 78.8531 sample estimates: mean of x 62.5 3. P-value computation for two sided tests. Let us continue the nicotine content example and ﬁnd the P-value for testing H : μ = 1 . 5 vs. H 1 : μ 6 = 1 . 5 . > 2*(1-pnorm(1.979899)) [1] 0.04771488 Review Problems. Example 8.17., 8.18....
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• Fall '04
• Chung
• Statistics, P-Values, Statistical hypothesis testing, H0, Student's t-distribution, Moo K. Chung

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