7 - STAT 350 Fall 2008 Homework #7 Solution through Lecture...

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STAT 350 – Fall 2008 Homework #7 – Solution through Lecture #11 Text Exercises Chapter 8, Problems #10, 12, 18, 40* * be sure to state the null and alternative hypotheses, give the value of the test statistic and the p - value. 8.10 a. no – do not reject H 0 b. no – do not reject H 0 c. yes – reject H 0 d. yes – reject H 0 e. no – do not reject H 0 f. yes – reject H 0 8.12 a. 34.43 34 2.868 1.06 50 z == p -value = 2P( Z > 2.868) = 2(1 - Φ (2.87)) = 2(1 – 0.9979) = 0.0042 b. 33.57 34 2.868 1.06 50 z p -value = 2P( Z < -2.868) = 2 Φ (-2.87)) = 0.0042 c. 33.25 34 2.2447 1.89 32 z p -value = 2P( Z < -2.24) = 2 Φ (-2.24)) = 0.025 d. 34.66 34 1.565 2.53 36 z p -value = 2P( Z > 1.565) = 2(1 - Φ (1.57)) = 2(1 – 0.9418) = 0.1164 8.18 a. With n = 15, df = 14 and the critical value of t for a one-tailed, α = 0.05 test, t critical = 1.761. Because the test statistic t is greater than the critical value, we would reject the null hypothesis in favor of the alternative hypothesis. The p -value for t is 0.003. b. With n = 9, df = 8 and the critical value of t for a one-tailed, α = 0.01 test, t critical = 2.896. Because the test statistic t is less than the critical value, we would fail to reject the null hypothesis . The p -value for t is 0.055. c. With n = 24, df = 23. Recall that only positive values of the test statistic would support the alternative hypothesis (because the alternative hypothesis is only supported if x > 20). Here there is no support for the alternative (t < 0). The p - value for t is 1 - 0.422 = 0.578. We would definitely fail to reject the null hypothesis . Homework #7 – Solution Page 1 of 6
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8.40 player ExpenditureIntake difference 1 14.4 14.6 -0.2 2 12.1 9.2 2.9 3 14.3 11.8 2.5 4 14.2 11.6 2.6 5 15.2 12.7 2.5 6 15.5 15 0.5 7 17.8 16.3 1.5 average 1.757 stdev 1.197 H 0 : μ d = 0, H a : d 0 1.757 0 3.8835 1.197 7 d d t sn −Δ == = df = 6, p -value = 0.004 × 2 = 0.008 We would reject the null hypothesis of no difference for a significance level of 0.05 or 0.01, but not for a significance level of 0.001.
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This note was uploaded on 02/23/2009 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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7 - STAT 350 Fall 2008 Homework #7 Solution through Lecture...

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