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FXSoln_F07 - ADM 2304 Solutions to Fall 2007 Final Exam 1(a...

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ADM 2304 Solutions to Fall 2007 Final Exam 1.(a) Two-sample T for Ott_Rents vs Que_Rents SE N Mean StDev Mean Ott_Rents 96 730 257 26 Que_Rents 57 534 200 26 Difference = mu (Ott_Rents) - mu (Que_Rents) Estimate for difference: 195.884 95% lower bound for difference: 134.224 T-Test of difference = 100 (vs >): T-Value = 2.57 P-Value = 0.006 DF = 140 -H0: mu(Ott)-mu(Que) <= 100, HA: mu(Ott) - mu(Que) > 100; -SE(diff) = sqrt(257^2/96 + 200^2/57) = 37.28 -t = ((730 - 534 ) - 100)/ 37.28 = 96 / 37.28 = 2.575 -Reject H0 if t > 2.326 -Decide to reject null H, conclude Ott Rents exceed Que Rents by > $100 Since both samples are large, we can use the z-approximation--hence, there is no need to assume equal variance to maximize d.f. If you do, then s(pooled) = 237.46, t = 2.42 and p-value = .008, based on df = 96 + 57 - 2 = 151 (treat as infinity). (b) Test and CI for Two Proportions (no pooled proportion) Sample X N Sample p 1 117 304 0.384868 2 52 191 0.272251 Difference = p (1) - p (2) Estimate for difference: 0.112617 95% lower bound for difference: 0.0425205 Test for difference = 0 (vs > 0): Z = 2.64 P-Value = 0.004 Test and CI for Two Proportions (pooled proportion) 95% lower bound for difference: 0.0425205 Test for difference = 0 (vs > 0): Z = 2.57 P-Value = 0.005 -H0: p(Ott) - p(Que) = 0, HA: p(Ott) - p(Que) > 0 -pooled p-hat = (117 + 52) / ( 304 + 191 ) = 169 / 495 = .34 -z = (117/304-52/191)/sqrt((.34*.66)*(1/304 + 1/191)) = .113/.044=2.575 -Reject H0 if z > 2.326 -Decide to reject null H, conclude there are more married people in Ott than Que (proportionately).
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Could be done as a chi-square test of equality of proportions (2-sided alternative) 1 117 187 304 103.79 200.21 1.681 0.872 2 52 139 191 65.21 125.79 2.676 1.387 Total 169 326 495 Chi-Sq = 6.616, DF = 1, P-Value = 0.010 Critical value is 6.635 based on 1 d.f. 2. Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts 1 2 3 4 5+ Total 1 22 27 30 42 14 135 24.30 33.75 24.98 36.45 15.53 0.218 1.350 1.011 0.845 0.150 2 14 23 7 12 9 65 11.70 16.25 12.03 17.55 7.48 0.452 2.804 2.100 1.755 0.311 Total 36 50 37 54 23 200 Chi-Sq = 10.996, DF = 4, P-Value = 0.027 (a) -H0: family size indep of religion, HA: family size assoc. with religion -chi-square contributions correct as above -chi-square statistic is 11 -critical value is 9.49, based on 4 df -reject null H, conclude family size is assoc. with religion -p-value is between .025 and .05 (closer to .025) (b) Name of Test Hypotheses Description and/or Comments
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