hw10sol

# hw10sol - STAT401 Homework 10 Solutions(Spring 2009 9.5.3 1...

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Unformatted text preview: STAT401: Homework 10 Solutions (Spring 2009) 9.5.3. 1. p-value is 1- Φ(1 . 61) = 1- . 9463 = 0 . 0537 9.6.4. 1. (a) β ( μ a ) = Φ μ- μ a σ/ √ n + z α Here, μ = 1, μ a = 2, α = . 05, σ = 4 . 1, Z . 05 = 1 . 645 The probability of type II error is: Φ 1- 2 4 . 1 / √ 36 + 1 . 645 = Φ(0 . 1815854) = 0 . 5720459 . (b) Note that H a : μ > 1, we need to use formulas below: n = σ ( z . 05 + z . 1 ) μ- μ a 2 Since our β = 0 . 1, Z β = 1 . 28 , α = 0 . 05, Z α = 1 . 645 that n = σ ( z . 05 + z . 1 ) μ- μ a 2 = 4 . 1(1 . 645 + 1 . 28) 1- 2 2 = 143 . 82 . The number of sample we need is n = 144. 10.4.3. 1. i. H : μ 1- μ 2 = 0 vs H a : μ 1- μ 2 6 = 0 ii. TS: Z = ¯ X 1- ¯ X 2 r S 2 1 n 1 + S 2 2 n 2 = 160592- 159778 q 3954 2 36 + 15533 2 42 = 0 . 33275 RR: | Z | ≥ z α/ 2 iii. No assumption for the distribution iv. z α/ 2 = z . 025 = 1 . 96 Since Z = 0 . 33 < 1 . 96 we fail to reject the null hypothesis....
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hw10sol - STAT401 Homework 10 Solutions(Spring 2009 9.5.3 1...

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