409Hw07ans - STAT 409 Fall 2009 Homework #7 ( Answers )...

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Unformatted text preview: STAT 409 Fall 2009 Homework #7 ( Answers ) 8.1-6 H : p = 1/6 vs. H 1 : p < 1/6 Left tailed. or H : p 1/6 vs. H 1 : p < 1/6 n = 8000. a) The test statistic is ( 29 ( 29 8000 6 1 1 6 1 6 1 8000 1-- =-- = y n n y z p p p . = 0.05. The critical (rejection) region is z < z = 1.645. b) y = 1265. The observed value of z (test statistic) ( 29 8000 6 1 1 6 1 6 1 8000 1265-- = z = 2.05 is less than 1.645 (the test statistic does fall into the rejection region) so Reject H . OR p-value = P(Z 2.05) = 0.0202 < 0.05 = , Reject H . c) ( 29 ( 29 - + = - + n p p z p 8000 8000 1265 1 8000 1265 645 . 1 8000 1265 , 1 , = [ , 0.1648 ]. 1 / 6 0.1667 is not in this interval. This is consistent with the conclusion to reject H . 8.1-8 The value of the test statistic is z = 390 25 . 75 . 75 . 70 . - = 2.280. a) Since z = 2.280 < 1.645, Reject H . b) Since z = 2.280 > 2.326, Do NOT Reject H . c) p-value = P(Z 2.280) = 0.0113. Note that 0.01 < p-value < 0.05. 8.1-10 a) H : p = 0.14 vs. H 1 : p > 0.14. Right tailed. b) The critical (rejection) region is z > z = 2.326, where ( 29 86 . 14 . 14 . 1 n n y n n y z p p p - =-- = . c) The observed value of z (test statistic) 590 86 . 14 ....
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409Hw07ans - STAT 409 Fall 2009 Homework #7 ( Answers )...

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