**Please go by the book: Principles by Biostatistics, Pagano, 2018. The answer is book based. pdf link available.

If you can, please use Rcommander (or other R programs) for problems below and please show me your work. Thank you.

Chapter 11, Problem 15 +

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 use 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 with congenital heart disease. The children had been randomized to one of two different treatment groups, known as "circulatory arrest" and "low-flow bypass." The groups differed in the specific way in which the reparative surgery was performed. Unlike circulatory arrest, low-flow bypass maintains continuous circulation through the brain; although it is felt to be preferable by some physicians, it also has its own risk of brain injury. The data contained in the data set heart. PDI scores are saved under the variable name pdi while MDI scores are saved under mdi and indicators of treatment group under trtment. For this variable, 0 represents circulatory arrest and 1 is for low-flow bypass.

a. For PDI, perform the group variance test to determine if the variances are similar for the two treatment groups. What do you conclude?

Treatment 0 (Circulatory Arrest):

60, 60, 63, 63, 63, 66, 67, 70, 70, 75, 76, 77, 78, 80, 80, 80, 80, 80, 80, 82, 82, 86, 86, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 92, 92, 92, 92, 92, 92, 93, 98, 98, 98, 98, 98, 98, 98, 98, 99, 99, 104, 104, 105, 105, 105, 105, 105, 105, 105, 105, 110, 111, 111, 111, 111, 111, 111, 117, 117, 122, 130, 134

N= 72

Treatment 1 (Low-flow bypass):

50, 52, 70, 75, 80, 80, 80, 80, 80, 86, 86, 87, 87, 90, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 93, 93, 93, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 99, 99, 99, 104, 104, 105, 105, 105, 109, 110, 110, 111, 111, 114, 115, 115, 115, 115, 117, 118, 118, 120, 122, 122, 122, 124

N = 70

b. At the 0.05 level of significance, test the null hypothesis that the mean PDI score at one year of age for the circulatory arrest treatment group is equal to the mean PDI score for the low-flow group. What is the p-value for this test?

c.For MDI, perform the group variance test to determine if the variances are similar for the two treatment groups. What do you conclude?

For MDI:

Treatment 0 (Circulatory arrest):

56, 58, 70, 74, 78, 78, 81, 82, 83, 86, 89, 89, 91, 91, 91, 91, 91, 93, 94, 96, 96, 96, 97, 98, 98, 98, 100, 100, 100, 100, 102, 102, 103, 103, 103, 103, 103, 103, 103, 106, 106, 106, 108, 108, 109, 109, 109, 110, 110, 112, 112, 112, 112, 114, 115, 115, 115, 115, 115, 115, 115, 115, 117, 117, 119, 122, 122, 130, 130, 131, 131, 140, 142

N = 73

Treatment 1 (Low-flow bypass):

50, 70, 78, 82, 83, 86, 86, 89, 91, 91, 93, 93, 96, 96, 96, 97, 97, 97, 98, 98, 100, 100, 102, 102, 103, 103, 103, 105, 106, 107, 107, 107, 107, 109, 109, 109, 109, 109, 109, 111, 112, 112, 112, 112, 112, 115, 115, 117, 117, 117, 117, 117, 117, 118, 118, 119, 119, 119, 119, 120, 120, 122, 122, 122, 122, 122, 124, 126, 130, 130

N = 70

d. Test the null hypothesis that the mean MDI scores are identical for the two treatment groups. What is the p-value?

e. What do these tests suggest about the relationship between a child's surgical treatment group during the first three months of life and his/her subsequent developmental status at one year of age?