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Unformatted text preview: 1 The ttest & TwoGroup Designs Hypothesis testing: One sample t test 95% 05 CI X t s X = ± . The confidence interval is the mean plus or minus a percentage of t times the standard error of the mean. S S N X X = The standard error of the mean is the standard deviation divided by the square root of N. S X X N X = − − ∑ ( ) 2 1 The standard deviation is the rootmeansquare deviation from the mean adjusted to be unbiased (with N1 in the denominator). We can use logic of the confidence interval to test (decide) whether a population mean has a certain value. For example suppose we know that the mean height of USF students is 68 inches. We want to test whether the mean height of women at USF is shorter than this. 80 70 60 50 40 Height in Inches 10 8 6 4 2 Frequency N=50 M = 63.05 SD=5.75 80 70 60 50 40 Height in Inches Pop Mean = 68 S X = .8 1 80 70 60 50 40 Height in Inches t=2.01 ci X = ± 163 . 80 70 60 50 40 Height in Inches One sample t test Confidence interval veiw 80 70 60 50 40 Height in Inches Histogram of Sample Height 2 70 62 15 12 9 6 3 Frequency t distribution view 62 Height in Inches One sample t test µ = 68 S X = .81 X = 6305 . t X S X = − = − = − µ 4 95 81 6 11 . . . X − = − µ 4 95 . t distribution Let's try another. Mean height= ? SD height =? N = 25 Confidence interval = xbar p/m (2.06)*(SD/5) t X S X = − µ Result?...
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 Fall '08
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