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Page 8 of 17 Use the following measurement scales for questions 10-15 We want to know whether different exam prep programs lead to different mean
Page 8 of 17 Use the following measurement scales for questions 10-15 We want to know whether different exam prep programs lead to different mean scores on a certain exam. To test, we recruit a number of students to participate in a study and randomly split them into three groups. The students in each group are assigned to one of the Analysis of Variance three exam prep programs for five weeks to prepare for the exam. At the end of the five weeks, all students take Source DF Adj SS Adj MS F-Value P-Value the same exam. (a = 0.05) Factor 2 333.3 166.66 3.80 0.034 Error 30 1315.6 43.85 Boxplot of Group1, Group2, Group3 Total 32 1648.9 100 Model Summary S R-sq R-sq(adj) R-sq(pred) 6.62207 20.21% 14.90% 3.46% 80 Means Factor N Mean StDev 95% CI 70 Group 1 11 81.77 8.45 (77.69, 85.85) Group2 11 89.24 5.72 (85.16, 93.32) Group3 11 83.60 5.24 (79.52, 87.68) 60 Group1 Group2 Group Pooled StDev = 6.62207 Probability Plot of Group1 Normal - 95% C Grouping Information Using the Tukey Method and 95% Confidence Factor N Mean Grouping Group2 11 89.24 A Group3 11 83.60 A B Group 1 11 81.77 B Percen Means that do not share a letter are significantly different. 70 BO 90 100 110 Tukey Simultaneous Tests for Differences of Means Probability Plot of Group2 Difference of Difference SE of Adjusted Normal - 95% C Levels of Means Difference 95% CI T-Value P-Value Group2 - Group1 7.47 2.82 (0.50, 14.44) 2.64 0.033 Group3 - Group1 1.83 2.82 (-5.14, 8.80) 0.65 0.794 Group3 - Group2 -5.64 2.82 (-12.60, 1.33) -2.00 0.131 Probability Plot of Group3 Normal -,95% CI Percent Individual confidence level = 98.05% TEST REP Percent . ... O.on What is the tota of students in the study?Page 9 of 17 a. Accept the null hypothesis. b. Do not reject the null hypothesis. c. Reject the null hypothesis and withhold judgment on the alternative hypothesis. d. Reject the null hypothesis and accept the alternative hypothesis. 13.(1/2) Again referring to the above output, which of the following statements best describes the conclusion that should be drawn? (Choose one) a. The test proves that the population mean test scores for all three groups are the same. b. While the test does not prove that the population means of the three groups are the same, it does provide convincing evidence that there are no differences. C. The population mean test score of Group2 is higher than that of both Group1 and Group3. d. The population mean test score of Group3 may not differ from that of either Group 1 or Group2, but the population mean of Group1 does differ from that of Group2. e. . The results provide convincing evidence that there is a difference in the true population mean test scores of each of the three groups. f. The results prove there is a difference in the true population mean test scores of each of the three groups. 14.(2) a) What assumptions were required to justify conducting the above analysis? (2) b) Do the assumptions appear to be reasonable in this case? (Explain your reasoning.) 15.(3) Briefly explain the meaning of this 'boxed-in' set of numbers (drawn from the printout shown above). Tukey Simultaneous Tests for Differences of Means Difference of Difference SE of Adjusted Levels of Means Difference 95% CI T-Value P-Value Group2 - Group 1 7.27 2.87 (0.19, 14.35) 2.53 0.043 Group3 - Group 1 1.82 2.87 (-5.26, 8.90) 0.63 0.803 Group3 - Group2 -5.45 2.87 (-12.54, 1.63) -1.90 0.156Page of 17 8 86 T E S T P R P Group2 Percent 8 8688 8 . . . 10.(1) What is the total number of students in the study? 1 1.(132) State the null and alternative hypotheses for this ANOVA in words (be specific) or in symbols. 70 Ho: Group 3 12.(112) Based on the above results, what conclusion should be drawn? (Choose one) a. Accept the null hypothesis. b. Do not reject the null hypothesis. c. Reject the null hypothesis and withhold judgment on the alternative hypothesis. d. Reject the null hypothesis and accept the alternative hypothesis. 13.(115) Again referring to the above output, which of the following statements best describes the conclusion that should be drawn? (Choose one) The test proves that the population mean test scores for all three groups are the same. b. While the test does not prove that the population means of the three groups are the same, it does provide convincing evidence that there are no differences. C. The population mean test score of Group2 is higher than that of both Group ] and Group3. d. The population mean test score of Group3 may not differ from that of either Group1 or Group2, but the population mean of Group1 does differ from that of Group2. e. The results provide convincing evidence that there is a difference in the true population mean test scores of each of the three groups. f . The results prove there is a difference in the true population mean test scores of each of the three groups
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