Question: This problem makes use of the attached SPSS data set heart. 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 attached SPSS data set heart; 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 PI score and the true mean MDI score for this population of children with congenital heart disease. Does either of these intervals contain the value 100? Would you have expected that they would?