ma316f03hw13

ma316f03hw13 - MA 316 MATHEMATICAL PROBABILITY...

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Unformatted text preview: MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT #13 SOLUTIONS: SECTIONS 6.2 and 6.3 (OPTIONAL) FALL 2003 6.14: If the observed value of ¯ X is 81.2 from a random sample of size n = 20 from N ( μ, 80), then a 95% confidence interval for μ is ¯ X- 1 . 96 σ √ n , ¯ X + 1 . 96 σ √ n ¶ = ˆ 81 . 2- 1 . 96 √ 80 √ 20 , 81 . 2 + 1 . 96 √ 80 √ 20 ! = (77 . 28 , 85 . 12) . 6.15: If ¯ X is the mean of a random sample of size n from a distribution that has mean μ and variance σ 2 = 10, then a 90% confidence interval for μ is ¯ X- 1 . 645 σ √ n , ¯ X + 1 . 645 σ √ n ¶ . Therefore if P ( ¯ X- 1 < μ < ¯ X + 1) = 0 . 90 then we must have 1 = 1 . 645 · 3 √ n . Solving for n gives n = 24 . 35 so let n = 25 . 6.16: If a random sample of size n = 17 from a normal distribution N ( μ,σ 2 ) yields ¯ x = 4 . 7 and s 2 = 5 . 76, we need to find a 90 percent confidence interval for μ . Since we don’t know μ or σ 2 we must use that the random variable T = ¯ X- μ S/ √...
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This note was uploaded on 09/10/2009 for the course STATS 517 taught by Professor Song during the Fall '07 term at Purdue.

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ma316f03hw13 - MA 316 MATHEMATICAL PROBABILITY...

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