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**Unformatted text preview: **HW5 Solution 6.10 σ is not known and n<30 => Definition 3 (a) 31.720 ; 8.729; 5 y mg s n = = = The standard error of the mean is 8.729 3.904 3.9 . 5 Y s SE mg n = = = ≈ (b) Sample size n=5 and the population standard deviation is not known. Therefore, we use Definition 3 in Lecture note 10&11. /2 /2 ( , ) s s x t x t n n α α- ⋅ + ⋅ The degree of freedom are n-1=5-1=4. We should find the 90% confidence interval, so α =.1 and /2 .05 2.776 t t α = = . The 90% confidence interval for μ is .05 .05 ( , ) 8.729 8.729 (31.720 2.776 , 31.720 2.776 ) 5 5 (23.4, 40.0) s s x t x t n n- ⋅ + ⋅ =- ⋅ + ⋅ = 6.12 σ is not known and n<30 => Definition 3 (a) 28.7; 4.5898; 4.5898 / 6 1.87 1.9 / . 28.7 (2.571)(1.9) (23.8,33,6) 23.8 33.6 / . y s SE g ml or g ml μ μ μ = = = = ≈ ± < < (b) μ = mean blood serum concentration of Gentamicin (1.5 hours after injection of 10mg/kg body weight) in healthy three-year-old female Suffolk sheep....

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