Unformatted text preview: [1] 1.644854 > qnorm(0.025) [1] 1.959964 Since z <z . 05 =1 . 64, we reject H at α = 0 . 05 level. 3. Testing mean μ with unknown variance σ 2 . H : μ = μ vs. H 1 : μ < μ Test statistic: t = ¯ xμ s/ √ n . Rejection region for level α test: z ≤ t α,n1 . Ex. IQ of a dog, X i ∼ N ( μ,σ 2 ) , where σ is unknown. Test H : μ = 100 vs. H 1 : μ < 100 at level α = 0 . 05. > t=(mean(x)100)/(sd(x)/sqrt(10)) > t [1] 4.205156 > qt(0.05,9) [1] 1.833113 A simpler method is to use command t.test . >help(t.test) ... t.test(x,alternative=c("two.sided", "less", "greater"),conf.level = 0.95) ... > t.test(x,mu=100,alternative="less", conf.level=0.95) One Sample ttest data: x t = 4.2036, df = 9, pvalue = 0.001147 alternative hypothesis: true mean is less than 100 95 percent confidence interval:Inf 78.8531 sample estimates: mean of x 62.5 Review problems Example 8.6., 8.7., 8.8., 8.9....
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 Fall '04
 Chung
 Statistics, Normal Distribution, Variance, Type I and type II errors, rejection region, Moo K. Chung

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