The Bayley Scales of Infant Development yield scores on two indices-the Psychomotor Development Index (PDI) and the Mental Development Index (MDI)- which can be used to assess a child's level of functioning in each of these areas at approximately one year of age. Among normal healthy infants, both indices have a mean value of 100. As part of a study assessing the development and neurologic status of children who have undergone reparative heart surgery during the first three months of life, the Bayley Scales were administered to a sample of one-year-old infants born with congenital heart disease. The data are contained in the data set heart [20] (Appendix B, Table B.l2); PDI scores are saved under the variable name pdi, while MDI scores are saved under mdi.

(a) At the 0.05 level of significance, test the null hypothesis that the mean PDI score for children born with congenital heart disease who undergo reparative heart surgery during the first three months of life is equal to 100, the mean score for healthy children. Use a two-sided test. What is the p-value? What do you conclude?

(b) Conduct the analogous test of hypothesis for the mean MDI score. What do you conclude?

(c) Construct 95% confidence intervals for the true mean PDI score and the true mean MDI score for this population of children with congenital heart disease. Does either of these intervals contain the value 1 00? Would you have expected that they would?

If needed and possible this course encourages the use of SPSS or I can use Excel. The data for the question is above.

TABLE B.12 Data set heart; variables trtment, pdi, and mdi 92 119 0 0 105 15 0 104 100 1 98 109 0 1 118124 1 122 109 0 80 98 106 92 126 98 106 92 117 93 107 77 109 1 105 103 86 0 10 15 0 105 103 1115 120 96 0 87 10210 0 111 130 11 119 92 81 93 131 87 1 105 82 115 99 112 86119 92 100 86 0 11 1000 86 0 105 140 1 15 118 1110 102 0 104 110 0 98 0 97 0 11 117 0 1114 118 0 0 0 105 104 112 0 117 106 92 109 93 102 0 1 103 0 134 131 86 100 97 0 0 122 115 92 115 92 130 70 98 117 0 78 108 0 92 115 86 112 0 86 115 92 103 86 103 0 1 124 122 82 115 107 87 960 96 0 80 70 109 98 0 130 114 0 105 112 92 92 142 80 112 1 122 109 107 86122 0 105 103 86 119 92 117 0 70 0 104 102 98 117 92 130 0 117 103 0 105 1030 98 109 92 122 92 108 92 1300 80 112 1 105 109 92 100 87 100 1 120 122 0 122 112 0 105 115 0 50 87 1120 67 106 50 1115 105 71 100 98 122 93 0 11 117 98 122 70 103 60 115 98 119 99 1070 1 11 109 0 87 112 76 110 0 98 1170 122 0 63 103 93 120