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 function in each of these areas at approximately one year of age. Among healthy infants, both indices have a mean value of 100. As part of 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 n = 144 of one-year-old infants born with congenital heart disease. These data are contained in the data file PDI-MDI.jmp and contain the following variables:

• PDI = psychomotor development index
• MDI = mental development index

Is there evidence 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 less than 100, which is the mean for healthy infants? Summarize your findings and check assumptions. Be sure to use both an appropriate test (report a p-value) and confidence interval to answer this question.

Distributions PDI Quantiles Summary Statistics Test Mean 100.0% maximum 134 Mean 94.783217 Hypothesized Value 100 99.5% 134 Std Dev 15.851041 Actual Estimate 94.7832 97.5% 122.8 Std Err Mean 1.3255306 DF 142 90.0% 115 Upper 95% Mean 97.40354 Std Dev 15.851 75.0% quartile 105 Lower 95% Mean 92.162893 t Test 50.0% median 98 N 143 Test Statistic -3.9356 25.0% quartile 86 Prob > It| 0.0001* 10.0% 75 Prob > t 0.9999 2.5% 60 Prob