data;

GPA,GMAT,PROGRAM 2.96,530,1 3.14,527,1 3.22,416,1 3.29,505,1 3.69,523,1 3.46,463,1 3.03,482,1 3.19,467,1 3.63,473,1 3.59,399,1 3.3,471,1 3.4,425,1 3.5,596,1 3.78,564,1 3.44,431,1 3.48,446,1 3.47,505,1 3.35,414,1 3.39,394,1 3.28,414,1 3.21,591,1 3.58,447,1 3.33,663,1 3.4,438,1 3.38,496,1 3.26,381,1 3.6,520,1 3.37,504,1 3.8,483,1 3.76,521,1 3.24,446,1 2.54,419,2 2.43,692,2 2.2,412,2 2.36,693,2 2.57,626,2 2.35,467,2 2.51,538,2 2.51,563,2 2.36,453,2 2.36,542,2 2.66,533,2 2.68,402,2 2.48,609,2 2.46,371,2 2.63,431,2 2.44,605,2 2.13,646,2 2.41,565,2 2.55,490,2 2.31,399,2 2.41,399,2 2.19,419,2 2.35,336,2 2.6,546,2 2.55,446,2 2.72,559,2 2.85,552,2 2.9,543,2 2.86,321,3 2.85,553,3 3.14,313,3 3.28,420,3 2.89,411,3 3.15,485,3 3.5,447,3 2.89,489,3 2.8,384,3 3.13,494,3 3.01,444,3 2.79,406,3 2.89,531,3 2.91,469,3 2.75,458,3 2.73,509,3 3.12,509,3 3.08,664,3 3.03,474,3 3.01,408,3 3.03,588,3 3.05,528,3 2.85,482,3 3.01,440,3 3.03,572,3 3.04,528,3

3) The admission office in a business school would like to test whether the mean undergraduate GPA and the mean GMAT scores are the same for incoming graduate students from three recruiting programs. The dataset is given in the datafile named Grad_Admission.txt in Exam One. Three recruiting programs are identified using 1, 2 and 3 in the dataset. a) Test the equality of mean vectors for the three programs at 5% significance level. b) If your test finds a difference in means, construct 95% simultaneous Bonferroni confidence intervals to determine which mean components differ among the populations represented by the three programs. c) Are the usual MANOVA assumptions (common covariance and multivariate normality) realistic for this data? Need to justify using p-values for appropriate tests. 3) The admission office in a business school would like to test whether the mean undergraduate GPA and the mean GMAT scores are the same for incoming graduate students from three recruiting programs. The dataset is given in the datafile named Grad_Admission.txt in Exam One. Three recruiting programs are identified using 1, 2 and 3 in the dataset. a) Test the equality of mean vectors for the three programs at 5% significance level. b) If your test finds a difference in means, construct 95% simultaneous Bonferroni confidence intervals to determine which mean components differ among the populations represented by the three programs. c) Are the usual MANOVA assumptions (common covariance and multivariate normality) realistic for this data? Need to justify using p-values for appropriate tests