Homework 4 Solutions - Solution for hw4 9-43 a 1 The...

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Solution for hw4 9-43 a) 1) The parameter of interest is the true mean battery life in hours, μ . 2) H 0 : μ = 40 3) H 1 : μ > 40 4) 5) Reject H 0 if z 0 > z α where α = 0.05 and z 0.05 = 1.65 6) , σ = 1.25 7) Because 1.26 < 1.65 fail to reject H 0 and conclude the battery life is not significantly greater than 40 at α = 0.05. b) P-value = c) = Φ (1.65 + - 5.06) = Φ (-3.41) 2245 0.000325 d) e) 95% Confidence Interval The lower bound of the 90 % confidence interval must be greater than 40 to verify that the true mean exceeds 40 hours. 9-46 a) 1) The parameter of interest is the true mean hole diameter, μ . 2) H 0 : μ = 1.50 3) H 1 : μ 1.50 4) 5) Reject H 0 if z 0 < - z α /2 where α = 0.01 and - z 0.005 = - 2.58 or z 0 > z α /2 where z 0.005 = 2.58 6) , σ = 0.01 7) Because - 2.58 < -1.25 < 2.58 fail to reject the null hypothesis. The true mean hole diameter is not significantly different from 1.5 in. at α = 0.01. b) P-value=2(1-)=2(1-)0.21 c) = Φ (5.08) - Φ (-0.08) = 1 – 0.46812 = 0.53188 power=1- β =0.46812. d) Set β = 1 - 0.90 = 0.10 n = = 2245 = 59.908, n 2245 60. e) For α = 0.01, z α /2 = z 0.005 = 2.58 1.4923 μ 1.5027 The confidence interval constructed contains the value 1.5. Therefore, there is not strong evidence that true mean hole diameter differs from 1.5 in. using a 99% level of confidence. Because a two-sided 99% confidence interval is equivalent to a two-sided hypothesis test at α = 0.01, the conclusions necessarily must be consistent.
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