Homework06Solutions

Homework06Solutions - CHEN 3010 Applied Data Analysis Fall...

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CHEN 3010 Applied Data Analysis Fall 2004 Homework 06 Solutions Problem 1 4-26. a) 1) The parameter of interest is the true mean ppm of benzene, μ . 2) H 0 : μ = 7980 3) H 1 : μ < 7980 4) α = 0.01 5) z x n 0 = μ σ / 6) Reject H 0 if z 0 < z α where z 0.01 = 2.33 7) x = 7906, σ = 80 925 . 2 10 / 80 7980 7906 0 = = z 8) Since -2.925 < -2.33, reject the null hypothesis and conclude manufacturers exit water meets federal regulation at α = 0.01. b) P-value = Φ (-2.925) 0.00172 c) critical x (for α = 0.01) = 05 . 7921 10 80 33 . 2 7980 0 = = n z σ μ α β => = = = > = < = <= = Px x Z x n ZZ critical critical [, ] . / (. ) . . 7920 80 1 7921 05 7920 80 10 10 042 1 0 516 0 484 Φ ΦΦ Or equivalently, using a formula not in your text, but from another text (J. L. Devore, “Probability and Statistics for Engineering and the Sciences” Sixth Edition, 2004) μμ = −− + 1 0 Φ z n true / for 0 1 : < H β = 1 7980 7920 10 80 001 + Φ z . () = 1 - Φ (-2.33 + 2.372) = 1 - Φ (0.042) = 0.4831 d) Set β = 1 0.90 = 0.10 n = zz δ + 22 2 = 2 2 2 10 . 0 01 . 0 ) 7980 7920 ( ) ( σ + z z 2 2 2 ) 60 ( ) 80 ( ) 29 . 1 33 . 2 ( + = 23.29, n 24. e) For α = 0.01, z α = z 0.01 = 2.33 + xz n .
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CHEN 3010 Applied Data Analysis Fall 2004 μ + 7906 2 33 80 10 . μ 7965 f) The confidence interval constructed does not contain the value 7980, thus the manufacturer’s exit water meets federal regulation using a 99% level of confidence.
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Homework06Solutions - CHEN 3010 Applied Data Analysis Fall...

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