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Consider a hypothesis test of H0: μ = 0 against H1: μ > 0 where μ is the mean percent change in total body bone mineral content of young women. The population standard deviation is σ = 2. The level of significance for the test is α = 0.05.
(For the prediction, just estimate the effect of increasing μ on the power in part (b) below.)
a) What sample size is minimally required to give at least 0.9 power? (Use Excel to calculate the power for a range of sizes for the SRS.) What is the actual power for this sample size?
b) Produce a power curve for a sample size of 25. A power curve is a scatter plot of power versus values of μ that are admissible under the alternative hypothesis. In order to produce a smooth curve, use Excel to calculate the power for μ ? {0.05, 0.10, 0.15, ..., 1.95, 2.00}, and direct Excel to connect the points in the scatter plot.
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Determine the rejection region for the test of Ho: (mean 1 - mean 2) > 2.43 Use a = 0.04. z >
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