# sol6 - HOMEWORK #6 SOLUTIONS 8.28(8.22-9.34) a) 1) The...

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HOMEWORK #6 SOLUTIONS 8.28(8.22-9.34) a) 1) The parameter of interest is the true mean life, μ . 2) H 0 : μ = 60000 3) H 1 : μ 60000 4) α = 0.05 5) t 0 = x s n - μ / 6) Reject H 0 if t 0 > t α ,n-1 where t 0.05,15 = 1.753 7) x = 60139.7 s = 3645.94 n = 16 t 0 = 60139 7 60000 364594 16 0153 . . / . - = 8) Since 0.153 < 1.753, do not reject the null hypothesis and conclude there is insufficient evidence to indicate that the mean life of this new tire is in excess of 60,000 km at α = 0.05. b) d = δ σ μ μ σ = - = - = 0 61000 60000 364594 0 274 . . Using the OC curve, Chart VIc) for α = 0.05, d = 0.274, and n = 16, we get β 2245 0.72 and power of 1 - 0.72 = 0.28. With the power being smaller than the acceptable level, 16 is not an adequate sample size for detecting a difference with probability of at least 0.90. c) t α ,n-1 = t 0.025,15 = 2.131 x t s n x t s n -  ≤ + 0 025 15 0 025 15 . , . , μ 60139 7 2131 364594 16 60139 7 2131 364594 16 . . . . . . -

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## This homework help was uploaded on 02/26/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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sol6 - HOMEWORK #6 SOLUTIONS 8.28(8.22-9.34) a) 1) The...

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