Hw_11_solutions_to_post - Andrea Gruber & Jery...

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Unformatted text preview: Andrea Gruber & Jery Stedinger Fall 2007 HW #11 Selection Solutions #7 Section 9.1, pg 334 (Devore 6, pg 370) 97 = M n , 4 . 10 = M , 83 . 4 = M s 148 = F n , 26 . 9 = F , 68 . 4 = F s H o : M = F, H a : M > F, = 5% M and F unknown, but have large samples Use standard normal test a) Hypothesis test Z = Z 0.05 = 1.645 ( 29 ( 29 83 . 1 148 68 . 4 97 83 . 4 26 . 9 4 . 10 2 2 2 2 = +-- = + -- = F F M M test n s n s F M Z > Z So we reject null hypothesis H o . The data indicates the average Boredom Proneness Rating is higher for males than for females. Also, for #7, if males = 10.5, and females = 9.5, with males = females = 5, b) What would be the type II error? 2 2 10.5 9.5 1.645 (0.114) 0.545 25 25 97 148 M F W M M W z n n -- = - = - = = + + c) What sample size n would result in a type II error of less than 10%? <0.1 ( 29 ( 29 2 ' 2 2 1 2 2 m n z z - + = + where ( 29 ' 1 2 a H = - and ( 29 1 2 H = - ' 10.5 9.5 1 =- = , = , 1.645 z = , 1.282 z = , 1 2 5 = = ( 29 ( 29 2 2 2 2 1 0 5 5 1.645 1.282 m n- + = + => ( 29 2 2 2 5 5 1 2.927 m n + = => 25 25 0.1167 m n + = If we assume that the two sample sizes are equal: m=n 25 25 0.1167 m m + = => 50 0.1167 m = => 428.4 429 m n = = #19 Section 9.2, pg 341-43 (Devore 6, pg 378-80) 1 6 n = , 1 115.7 x = , 1 5.03 s = 2 6 n = , 2 129.3 x = , 2 5.38 s = 1 2 : 10 H - = - 1 2 : 10 a H - < - Andrea Gruber & Jery Stedinger Fall 2007 0.01 = a) For the given hypotheses, the test statistic 20 . 1 007 . 3 6 . 3 10 3 . 129 7 . 115 6 38 . 5 6 03 . 5 2 2- =- = + +- = t ( 29 ( 29 ( 29 96 . 9 5 8241 . 4 5 2168 . 4 8241 . 4 2168 . 4 2 2 2 = + + = , so use d.f. = 10. We will reject H if .01,10 2.764; t t n- = - since 1.20 > -2.764, we dont reject H . b) If the true means are 115 and 133, and both st devs = 5.0, what is the type II error for an =1% test. ( 29 ( 29 2 2 1 2 1 2 1 a d n n- + = + + => ( 29 ( 29 2 2 (115 133) ( 10) 5 5 10 1 6 6 d-- + - = + + => d=0.84 Go to table A.17 to find : find that is between 0.5 and 0.4, about 0.45 P1) After two structural engineering firms merged, an internal review obtained the two firms bids on 8 recent projects. Is there any significant difference between the firms estimated costs? Project Firm W Firm V W-V 1 177.0 131.0 46.0 2 2,230.0 1,400.0 830.0 3 129.0 78.0 51.0 4 11.2 11.9-0.7 5 338.0 298.0 40.0 6 266.0 170.0 96.0 7 612.0 656.0-44.0 8 408.0 282.0 126.0 Average 521.4 378.4 143.0 Stand. Dev. 714.4 457.6 282.5 i D = i i V W- , the difference between the 1 st and 2 nd observations within a pair n = 8, 143 = D , 5 . 282 = D s a) What are the appropriate null and alternative hypotheses?...
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This note was uploaded on 02/02/2008 for the course CEE 3040 taught by Professor Stedinger during the Fall '08 term at Cornell University (Engineering School).

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Hw_11_solutions_to_post - Andrea Gruber & Jery...

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