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Unformatted text preview: APPM 4/5570 Solutions to Problems from Section 8.2 19. a. Step One: State the hypotheses. Done! Step Two: Write down the test statistic. Z = X μ σ/ √ n = 94 . 32 95 1 . 2 / 4 ≈  2 . 27 Step Three: Find the rejection region. The rejection region is twotailed. It is the region under the standard normal ( Z ) curve above 2 . 57 and below 2 . 57. (These are the critical values that capture 0 . 01 / 2 = 0 . 005 “above” and “below”.) Step Four: The test statistic is not in the rejection region. Therefore, we fail to reject H in favor of H a at 0 . 01 level of significance. There is not evidence in the data to suggest that the true mean melting point is different from 95. (Note that we did not “prove” that it is 95, we just can’t disprove it.) b. β (94) = P ( fail to reject H when μ = 94 ) We fail to reject if the test statistic from part (a) is between 2 . 57 and 2 . 57. That is, if 2 . 57 ≤ X 95 1 . 2 / 4 ≤ 2 . 57 or, equivalently, 94 . 229 ≤ X ≤ 95 . 771 . Returning to the β (94) calculation, β (94) = P ( fail to reject H when μ = 94 ) = P (94 . 229 ≤ X ≤ 95 . 771 when μ = 94) = P 94 . 229 94 1 . 2 / 4 ≤...
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 '08
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 Normal Distribution, rejection region

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