mont4e_sm_ch09_sec02

# mont4e_sm_ch09_sec02 - Section 9-2 9-29 a H 0 = 10 H 1 > 10...

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9-10 Section 9-2 9-29 a) 10 : , 10 : 1 0 > = μ H H b) 7 : , 7 : 1 0 = H H c) 5 : , 5 : 1 0 < = H H 9-30 a) α =0.01, then a= 2 / α z =2.57 and b=- 2 / z =-2.57 b) α =0.05, then a= 2 / z =1.96 and b=- 2 / z =-1.96 c) α =0.1, then a= 2 / z =1.65 and b=- 2 / z =-1.65 9-31 a) α =0.01, then a= z 2.33 b) α =0.05, then a= z 1.64

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9-11 c) α =0.1, then a= α z 1.29 9-32 a) α =0.01, then a= 1 z -2.33 b) α =0.05, then a= 1 z -1.64 c) α =0.1, then a= 1 z -1.29 9-33 a) p-value=2(1- ) ( 0 Z Φ )=2(1- ) 05 . 2 ( Φ ) 0.04 b) p-value=2(1- ) ( 0 Z Φ )=2(1- ) 84 . 1 ( Φ ) 0.066 c) p-value=2(1- ) ( 0 Z Φ )=2(1- ) 4 . 0 ( Φ ) 0.69 9-34 a) p-value=1- ) ( 0 Z Φ =1- ) 05 . 2 ( Φ 0.02 b) p-value=1- ) ( 0 Z Φ =1- ) 84 . 1 ( Φ 0.97 c) p-value=1- ) ( 0 Z Φ =1- ) 4 . 0 ( Φ 0.34 9-35 a) p-value= ) ( 0 Z Φ = ) 05 . 2 ( Φ 0.98 b) p-value= ) ( 0 Z Φ = ) 84 . 1 ( Φ 0.03 c) p-value= ) ( 0 Z Φ = ) 4 . 0 ( Φ 0.65 9-36 a.) 1) The parameter of interest is the true mean water temperature, μ . 2) H 0 : μ = 100 3) H 1 : μ > 100 4) α = 0.05 5) z x n 0 = −μ σ / 6) Reject H 0 if z 0 > z α where z 0.05 = 1.65 7) 98 = x , σ = 2 0 . 3 9 / 2 100 98 0 = = z 8) Since -3.0 < 1.65 do not reject H 0 and conclude the water temperature is not significantly different greater than 100 at α = 0.05. b) P-value = 99865 . 0 00135 . 0 1 ) 0 . 3 ( 1 = = Φ c) + Φ = 9 / 2 104 100 05 . 0 z β = Φ (1.65 + 6) = Φ (-4.35) 0 9-37 a) 1) The parameter of interest is the true mean crankshaft wear, μ . 2) H 0 : μ = 3 3) H 1 : μ 3 4) α = 0.05 5) z x n 0 = σ / 6) ) Reject H 0 if z 0 < z α /2 where z 0.025 = 1.96 or z 0 > z α /2 where z 0.025 = 1.96
9-12 7) x = 2.78, σ = 0.9 95 . 0 15 / 9 . 0 3 78 . 2 0 = = z 8) Since –0.95 > -1.96, do not reject the null hypothesis and conclude there is not sufficient evidence to support the claim the mean crankshaft wear is not equal to 3 at α = 0.05. b) + Φ + Φ = 15 / 9 . 0 25 . 3 3 15 / 9 . 0 25 . 3 3 025 . 0 025 . 0 z z β = Φ (1.96 + 1.08) Φ ( 1.96 + 1.08) = Φ (0.88) Φ (-3.04) = 0.81057 (0.00118) = 0.80939 c) () ( ) , 21 . 15 ) 75 . 0 ( ) 9 . 0 ( ) 29 . 1 96 . 1 ( ) 3 75 . 3 ( 2 2 2 2 2 2 10 . 0 025 . 0 2 2 2 2 / = + = + = + = σ δ α z z z z n 16 n 9-38 a) 1) The parameter of interest is the true mean melting point, μ .

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mont4e_sm_ch09_sec02 - Section 9-2 9-29 a H 0 = 10 H 1 > 10...

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