HW 10 - STAT 400 Homework #10 ( due Friday, November 11, by...

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STAT 400 Homework #10 Fall 2011 ( due Friday, November 11, by 3:00 p.m. ) From the textbook: 6.6-12 ( ) a) … if we believe the seed distributor’s claim; b) … if we ignore the seed distributor’s claim. a) … if we believe the seed distributor’s claim; n = 20 0 80 0 03 0 645 1 2 . . . . = 481.0711. Round up. n = 482. b) … if we ignore the seed distributor’s claim. n = 50 0 50 0 03 0 645 1 2 . . . . = 751.673611. Round up. n = 752. 7.1-8 ( ) The value of the test statistic is z = 390 25 . 0 75 . 0 75 . 0 70 . 0 - = – 2.280. a) Since z = – 2.280 < – 1.645, Reject H 0 . b) Since z = – 2.280 > – 2.326, Do NOT Reject H 0 . c) p-value = P(Z 2.280) = 0.0113. Note that 0.01 < p-value < 0.05.
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7.1-10 ( ) a) H 0 : p = 0.14 vs. H 1 : p > 0.14. Right – tailed. b) The critical (rejection) region is z > z α = 2.326, where ( ) 86 . 0 14 . 0 14 . 0 1 0 0 0 n n y n n y z p p p - = - - = . c) The observed value of z (test statistic) 590 86 . 0 14 . 0 14 . 0 590 104 - = z = 2.539 is greater than 2.326 (the test statistic does fall into the rejection region) so Reject H 0 . OR p-value = P(Z 2.539) 0.0055 < 0.01 = α , Reject H 0 . We conclude that the campaign was successful. 7.1-12 ( ) a) ( ) 35 . 0 65 . 0 65 . 0 1 0 0 0 n n y n n y z p p p - = - - = > 1.96. b) 600 35 . 0 65 . 0 65 . 0 600 414 - = z = 2.054 > 1.960, so Reject H 0 at α = 0.025. c) p-value = P(Z 2.054) = 0.0200 < 0.0250 = α , so Reject H 0 at α = 0.025. d) A 95% one-sided confidence interval for p is ( ) - = - - 1 , 600 31 . 0 69 . 0 645 . 1 69 . 0 1 , ˆ 1 ˆ ˆ n p p z p α = [ 0.659 , 1 ].
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7.1-18 ( ) n 1 = 605, y 1 = 351. 605 351 ˆ 1 1 1 = = n y p 0.58. n 2 = 195, y 2 = 41. 195 41 ˆ 2 2 2 = = n y p 0.21. 800 392 195 605 41 351 ˆ 2 1 2 1 = + + = + + = n n y y p = 0.49. a) H 0 : p 1 = p 2 vs. H 1 : p 1 p 2 . Two – tailed. The test statistic is ( ) n n p p p p z + - - = 2 1 2 1 1 1 ˆ 1 ˆ ˆ ˆ , where 2 1 2 2 1 1 2 1 2 1 ˆ ˆ ˆ n n p n p n n n y y p + + = + + = . α
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HW 10 - STAT 400 Homework #10 ( due Friday, November 11, by...

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