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Unformatted text preview: Statistics 403 Problem Set 3 Due in lab on Friday, October 1st 1. Suppose we are interested in estimating a quantity μ , and we can obtain independent measurements X i with EX i = μ . We intend to use ¯ X to estimate μ , and we wish to have the probability of the estimation error being greater than 0 . 1 units be equal to 0.1. What sample size is required if the standard deviation σ = SD( X i ) is (i) σ = 0 . 5 or (ii) σ = 0 . 2? You can treat ¯ X as being normally distributed. Solution: For this problem, I was thinking of the error as being the absolute difference between the estimate and the true value, | ¯ X- μ | . But if you use the signed error ¯ X- μ , that’s OK this time. The following calculation gives the probability of the absolute error being greater than . 1 units: P ( | ¯ X- μ | > . 1) = 2 P ( ¯ X- μ > . 1) = 2 P ( √ n ¯ X- μ σ > . 1 √ n/σ ) = 2 P ( Z > . 1 √ n/σ ) We want an error larger than 0.1 to occur only 0.1 fraction of the time, so we set 2 P ( Z > . 1...
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