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# 409Hw04ans - STAT 409 Fall 2005 Homework#4(due Friday...

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STAT 409 Fall 2005 Homework #4 (due Friday, September 25, by 4:00 p.m.) From the textbook: 6.4-8 a) x = 46.42 ; b) s 2 = 41.682, s 6.456, t 0.05 ( 4 ) = 2.132, 5 456 . 6 132 . 2 42 . 46 ± or 46.42 ± 6.156 or ( 40.264, 52.576 ) . 6.4-10 t 0.10 ( 27 ) = 1.314, ( ( , 28 31 . 0 314 . 1 45 . 21 - = ( 21.373, . 6.4-12 a) x = 3.580 ; b) s 0.512 , c) t 0.05 ( 9 ) = 1.833, ( 10 512 . 0 833 . 1 580 . 3 , 0 ± = ( 0, 3.877 ) .

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6.4-18 n = 1219 – large, use z 0.005 to approximate t 0.005 ( 1218 ) . z 0.005 = 2.576, ( 1219 02 . 0 576 . 2 05 . 6 ± or 6.05 ± 0.0015 or ( 6.0485, 6.0515 ) . 6.8-2 n = ( ( ( 29 2 2 5 . 1 169 96 . 1 = 288.547 so the sample size needed is 289 . 6.8-4 n = ( ( ( 29 2 2 5 . 0 9 . 34 96 . 1 = 536.28736 so the sample size needed is 537 . Then use 537 2 New New s z x α ± = 537 96 . 1 New New s x ± . OR t 0.025 ( 28 ) = 2.048; n = ( ( ( 29 2 2 5 . 0 9 . 34 048 . 2 = 585.5248384 so the sample size needed is 586 . Then use ( 29 586 28 2 Old New s t x α ± = 586 9 . 34 048 . 2 ± New x .
6.8-6 n = ( ( ( 29 2 2 2 5 7 . 33 96 . 1 = 174.51466816 so the sample size needed is 175 . 6.5-2 “Hint”: Equal variances x ( x x - ) 2 y ( y y - ) 2 644 493 532 462 565 10983.04 2134.44 51.84 5959.84 665.64 623 472 492 661 540 502 549 518 6142.640625 5274.390625 2769.390625 13543.140625 21.390625 1816.890625 19.140625 708.890625 Total: 2696 19794.80 4357 30295.875000 x = 5 2696 = 539.2, s x 2 = 4 8 . 19794 = 4948.7, y = 8 4357 = 544.625, s y 2 = 7 875 . 30295 4327.982. ( ( 2 8 5 982 . 4327 1 8 7 . 4948 1 5 2 pooled - + - - = s 4553.7, pooled s 67.481. t 0.05 ( 11 ) = 1.796, ( 29 8 1 5 1 481 . 67 796 . 1 625 . 544 2 . 539 + ± - 5.425 ± 69.092 or ( 74.517, 63.667 ) .

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6.5-4 x ( x x - ) 2 y ( y y - ) 2 1612 1352 1456 1222 1560 1456 1924 10057.2245 25508.6531 3104.0816 83934.3673 2331.5102 3104.0816 169979.5102 1082 1300 1092 1040 910 1248 1092 1040 1092 1288 1324.96 32978.56 696.96 6146.56 43430.56 16796.16 696.96 6146.56 696.96 28764.16 Total: 10582 298019.4285 11184 137678.40 (a) x = 7 10582 = 1511.714, y = 10 11184 = 1118.400, x y = 1511.714 – 1118.400 = 393.314; (b) s x 2 = 6 4285 . 298019 49669.905, s y 2 = 9 40 . 137678 = 15297.600. - + - + 1 1 1 1 2 2 2 2 2 2 1 2 1 1 2 2 2 2 1 2 1 n n n n n n s s s s =
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409Hw04ans - STAT 409 Fall 2005 Homework#4(due Friday...

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