sol.hw8.stat3011 - Homework 8 Solutions Yicheng Kang 8.30 >...

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Homework 8 Solutions Yicheng Kang November 11, 2010 8.30 > x=c(11,11,6,9,14,-3,0,7,22,-5,-4,13,13,9,4,6,11) > mean(x) [1] 7.294118 > sd(x) [1] 7.183007 > sd(x)/sqrt(length(x)) [1] 1.742135 > qt(.975,length(x)-1) [1] 2.119905 > t.test(x,conf.level=.95) One Sample t-test data: x t = 4.1869, df = 16, p-value = 0.0006974 alternative hypothesis: true mean is not equal to 0 1
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95 percent confidence interval: 3.600956 10.987279 sample estimates: mean of x 7.294118 > mean(x)-qt(.975,length(x)-1)*(sd(x)/sqrt(length(x))) [1] 3.600956 > mean(x)+qt(.975,length(x)-1)*(sd(x)/sqrt(length(x))) [1] 10.98728 8.36 a)The confidence intervals refers to means, not individual scores. b)This should say, if random samples of 9 women were repeatedly selected, then 95% of the time, the confidence interval would contain the population mean. c)We KNOW that ¯ x falls in the confidence interval; this is the sample mean on which the confidence interval is based. d)If we sample the entire population and take the mean, we are going to get the exact mean of the population. 8.51 a) n = σ 2 z 2 m 2 = 200 2 × 1 . 96 2 25 2 = 246 b) We can use the same formula as in part (a).
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