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

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Stat 312: Lecture 12 Testing on Population Proportion Moo K. Chung [email protected] Feb 20, 2003 Concepts 1. Testing mean μ when the sample size is large. H 0 : μ = μ 0 vs. H 1 : μ < μ 0 Test statistic: z = ¯ x - μ 0 s/ n . Rejection region for level α test: z ≤ - z α . 2. Let p be the proportion of a population with a specified property. Large-sample level α test for H 0 : p = p 0 vs. H 1 : p < p 0 test statistic: z = ˆ p - p 0 p 0 (1 - p 0 ) /n . rejection region: z < - z α . 3. The P -value is the smallest level of significance at which H 0 would be rejected. 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 H 0 . In-class problems Example 8.11. 47 out of 102 doctors did not know the generic name for the drug methadone. Can you conclude that fewer than half of all doctors know the generic name for methadone? Test it at 1% level. > p<-47/102 > (p-0.5)/sqrt(0.5*0.5/102) [1] -0.792118 > qnorm(0.01) [1] -2.326348 Assume the IQ of a dog follows normal. The IQs of 10 dogs are measured: 30, 25, 70, 110, 40, 80, 50,
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Unformatted text preview: 60, 100, 60. ±ind the P-value for testing H : μ = 100 vs. H 1 : μ < 100 > t=(mean(x)-100)/(sd(x)/sqrt(10)) > t [1] -4.205156 > qt(c(0.001,0.002,0.003),9) [1] -4.296806 -3.834510 -3.572577 > pt(-4.205156,9) [1] 0.001144577 > 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 Three options for alternative:less, greater, two.sided . ±ind the P-value for testing H : μ = 100 vs. H 1 : μ 6 = 100 Self-study problems Exercise 8.35., Example 8.17., ±ind the P-value for testing H : μ = 100 vs. H 1 : μ > 100 Assignment 4. Due March 13. 11:00am. 8.24., 8.26, 8.28., 8.36. (a) and (b) only, 8.38....
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