Computer & Data Analysis- Dr. Samir Safi & Mr. Ibrahim Abed Midterm Exam 2- Nov. 26, 2013 Student’s Name: Student ID #: Question #1: (10 Points) A chain of convenience stores wanted to test three different advertising policies: Policy 1: No advertising. Policy 2: Advertise in neighborhoods with circulars. Policy 3: Use circulars and advertise in newspapers. Eighteen stores were randomly selected and divided randomly into three groups of six stores. Each group used one of the three policies. Following the implementation of the policies, sales figures were obtained for each of the stores during a 1-month period. Using the SPSS output and .05 , give an interpretation for each of the following: 1. (2 Points) Test of Homogeneity of Variances. 2. (2 Points) Explain in details the result of the ANOVA Table. 3. (6 Points) Discuss all the multiple comparisons. 1 SPSS Output for question #1 Test of Homogeneity of Variances DATA Levene Statistic .841 df1 df2 2 Sig. .451 15 ANOVA DATA Between Groups W ithin Groups Total Sum of Squares 115.111 101.167 216.278 df 2 15 17 Mean Square 57.556 6.744 F 8.534 Sig. .003 Multiple Comparisons Dependent Variable: DATA Bonferroni (I) GROUP Policy 1 Policy 2 Policy 3 (J) GROUP Policy 2 Policy 3 Policy 1 Policy 3 Policy 1 Policy 2 Mean Difference (I-J) -.6667 -5.6667* .6667 -5.0000* 5.6667* 5.0000* Std. Error 1.49938 1.49938 1.49938 1.49938 1.49938 1.49938 *. The mean difference is s ignificant at the .05 level. 2 Sig. 1.000 .005 1.000 .014 .005 .014 95% Confidence Interval Lower Bound Upper Bound -4.7056 3.3723 -9.7056 -1.6277 -3.3723 4.7056 -9.0389 -.9611 1.6277 9.7056 .9611 9.0389 Question #2: (10 Points) An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm- infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After a 6-month period, the lambs were slaughtered and the following worm counts were recorded: Drug-Treated Sheep 18 43 28 50 16 32 13 35 38 33 6 7 Untreated Sheep 40 54 26 63 21 37 39 23 48 58 28 39 Using .05 and the SPSS output, give an interpretation for each of the following: a. (3 Points) What's the suitable statistical technique? b. (7 Points) Test whether the mean number of tapeworms in the stomachs of the treated lambs is less than the mean for untreated lambs. Assume the data is normally distributed for each group. 3 SPSS Output for question #2 Group Statistics Worm counts CODING Drug-Treated Sheep Untreated Sheep N Mean 26.5833 39.6667 12 12 Std. Deviation 14.36193 13.85859 Std. Error Mean 4.14593 4.00063 Independent Samples Test Levene's Test for Equality of Variances F Worm counts Equal variances as sumed Equal variances not ass umed t-test for Equality of Means Sig. .205 t .655 df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper -2.271 22 .033 -13.0833 5.76141 -25.03176 -1.13491 -2.271 21.972 .033 -13.0833 5.76141 -25.03264 -1.13403 Paired Samples Statistics Pair 1 Drug-Treated Sheep Untreated Sheep Mean 26.5833 39.6667 N 12 12 Std. Error Mean 4.14593 4.00063 Std. Deviation 14.36193 13.85859 Paired Samples Correlations N Pair 1 Drug-Treated Sheep & Untreated Sheep Correlation 12 .583 Sig. .046 Paired Samples Test Paired Differences Mean Pair 1 Drug-Treated Sheep - Untreated Sheep -13.0833 Std. Deviation Std. Error Mean 12.88733 3.72025 4 95% Confidence Interval of the Difference Lower Upper -21.2716 -4.8951 t -3.517 df Sig. (2-tailed) 11 .005 Question #3: (5 Points) Do rates of smoking decrease from pre-intervention to post-intervention? State your hypotheses and explain in details your findings by using SPSS at 0.05 level? SPSS Output for question #3 Paired Samples Statistics Pair 1 Mean 30.53 5.43 Mean # of cigarettes smoked per day Pre-intervention Mean # of cigarettes smoked following intervention N 30 30 Std. Error Mean .987 1.108 Std. Deviation 5.406 6.067 Pa ired Sa mples Test Mean Pair 1 Mean # of cigarettes smoked per day Pre-intervention 25.100 - Mean # of cigarettes smoked following intervention 5 Paired Differences 95% Confidence Interval of the Difference Std. Error Std. Deviation Mean Lower Upper 7.402 1.351 22.336 27.864 t 18.574 df Sig. (2-tailed) 29 .000 Question #4: (15 Points) The data set BP contains blood pressure and other vital signs during various physical and mental stressors. Using 0.05 and the SPSS output, give an interpretation for each of the following: a. (5 Points) Test the assumption of homogeneity b. (15 Points) Does the mean of heart rate while immersing a hand in ice water (hrcp) vary to a person's sex, parental hypertension (PH), or some combination of these factors? Explain all related results. 6 SPSS Output for question #4 a Le vene's Test of Equa lity of Error Va riances Dependent Variable: heart rate cold pressor F 1.352 df1 3 df2 176 Sig. .259 Tests the null hypothes is that t he error variance of the dependent variable is equal across groups. a. Design: Int ercept+s ex+ ph+ sex * ph Tests of Between-Subjects Effects Dependent Variable: heart rate cold press or Source Corrected Model Intercept sex ph sex * ph Error Total Corrected Total Type III Sum of Squares 1664.321a 1265221.332 1235.279 344.518 38.408 40744.540 1311649.000 42408.861 df Mean Square 554.774 1265221.332 1235.279 344.518 38.408 231.503 3 1 1 1 1 176 180 179 F 2.396 5465.247 5.336 1.488 .166 Sig. .070 .000 .022 .224 .684 a. R Squared = .039 (Adjus ted R Squared = .023) Pa irw ise Com parisons Dependent Variable: heart rate cold pressor (I) subject sex female male (J) subject sex male female Mean Difference (I-J) St d. Error 5.244* 2.270 -5. 244* 2.270 a Sig. .022 .022 95% Confidenc e Interval for a Difference Lower Bound Upper Bound .764 9.724 -9. 724 -.764 Based on estimated marginal means *. The mean differenc e is significant at the .05 level. a. Adjust ment for multiple comparisons: Bonferroni. Pairwise Comparisons Dependent Variable: heart rate cold press or (I) parental hypertension PH PH + (J) parental hypertension PH + PH - Mean Difference (I-J) -2.769 2.769 Std. Error 2.270 2.270 a Sig. .224 .224 95% Confidence Interval for a Difference Lower Bound Upper Bound -7.250 1.711 -1.711 7.250 Based on estimated marginal means a. Adjustment for multiple comparis ons : Bonferroni. 3. subject sex * parental hyperte nsion Dependent Variable: heart rate cold pressor subjec t sex female male parent al hy pert ens ion PH PH + PH PH + Mean 84.689 88.383 80.370 82.214 St d. Error 2.268 2.219 2.243 2.348 7 95% Confidenc e Interval Lower Bound Upper Bound 80.213 89.165 84.003 92.763 75.942 84.797 77.581 86.848