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# 409EC - of the Red Army soldiers is 82 kg H μ = 85 vs H 1...

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STAT 409 Extra Credit (3 points) Fall 2011 1. The Red Army Manual states that the overall average weight of the Red Army soldiers must be 85 kg. A Red Army general wishes to test whether the overall average is as is specified by the Manual. That is, he wishes to test H 0 : μ = 85 vs. H 1 : μ 85. Suppose he knows that the weights of the Red Army soldiers are approximately normally distributed, with overall standard deviation 10 kg. Suppose we plan to obtain a random sample of 9 soldiers to perform this test. Since the Red Army Day is February 23, the general insists on the significance level of 23.02%. Find the power of this test if the true overall average weight
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Unformatted text preview: of the Red Army soldiers is 82 kg. H : μ = 85 vs. H 1 : μ ≠ 85 2 – tailed. α = 0.2302. α / 2 = 0.1151. 2 α z = z 0.1151 = 1.20 . Rejection Region: Reject H if Z = σ μ X n-< 2 α z-or Z = σ μ X n-> 2 α z ⇒ σ μ 2 α X n z-< or σ μ 2 α X n z + > ⇒ 9 10 20 . 1 85 X-< or 9 10 20 . 1 85 X + > ⇒ 81 < X or 89 > X Power = P ( Reject H | H is false ) = P ( 81 X < | μ = 82 ) + P( 89 X > | μ = 82 ) = -> + -< 9 10 82 89 Z P 9 10 82 81 Z P = P ( Z < – 0.30 ) + P( Z > 2.10 ) = 0.3821 + 0.0179 = 0.40 ....
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