Sec_11_solutions__11_19_04_

Sec_11_solutions__11_19_04_ - CEE 304 Section#11 Handout...

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CEE 304 – Section #11 Handout (11-17-04) Hypothesis Testing Examples: Two-Sample Test vs. Paired Data Test 1. Sample Final Exam Question: Professor Stedinger’s TQM project team decided to investigate the claim that professor X really assigned more homework than professor Y. They randomly chose 8 students from each class (16 students all together) and had them record the length of time they spent on homework over two weeks. The data look like: Students with X Students with Y 22.8 13.0 15.9 12.9 13.7 11.9 15.7 14.9 23.1 14.1 15.5 19.7 19.1 9.1 9.4 15.4 _______ ________ Average: 16.90 13.88 St. Dev.: 4.61 3.07 a.) What are the appropriate null and alternative hypotheses? H o : μ X = μ Y H a : μ X > μ Y b.) What is the rejection region for a t-test with a type I error of 5%? Reject H o if T test ≥ t α,υ Where 2 2 ( ) ( ) X Y test y x x y X Y T s s n n μ μ - - - = + And 2 2 2 2 2 2 4 4 4 4 2 2 2 2 4.61 3.07 8 8 12.2 12 4.61 3.07 8 8 8 1 8 1 1 1 y x x y y x y x x y s s n n s s n n n n υ + + = = = 2245 + + - - - - So, Reject H o if T test ≥ t 0.05,12 = 1.782 c.) What is the p-value for this data? 2 2 (16.90 13.88) 0 1.542 4.61 3.07 8 8 test T - - = = +
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p-value = Pr[t ≥ T test | υ] = Pr[t ≥ 1.542 | υ = 12] = 0.075 What do you conclude based on this data? p-value = 0.075 > α = 0.05 Fail to reject H o at the 5% level Or, T test = 1.542 < t 0.05,12 = 1.782 Fail to reject H o at the 5% level d.) If the true means are μ x = 17 and μ Y = 13.5, both with standard deviation, σ = 4, what is the probability of a type II error for the test in part (b)?
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