The Bayley Scales of Infant Development yield scores on two indices – the Psychomotor Development Index (PDI) and the Mental Development Index (MDI) – that can be used to assess a child’s level of functioning at approximately one year of age. Among normal healthy infants, both indices have a mean value of 100. As part of a study investigating the development and neurologic status of children who had 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 failure. 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 associated risk of brain injury. Sample N Mean MDI scores St. Dev Low flow By-Pass Group 70 106.4 212.3594 Circulatory Arrest Group 73 103.0822 274.382 Assume that the MDI scores are approximately normally distributed in each group. At the 5% significance level, test the null hypothesis that the mean MDI score at one year of age for the circulatory arrest treatment group is equal to the mean MDI score for the low-flow group. Also provide and interpret the corresponding 95% confidence interval. Define the parameter(s) of interest. State the null and alternative hypotheses. State the significance level.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Bayley Scales of Infant Development yield scores on two indices – the Psychomotor Development Index (PDI) and the Mental Development Index (MDI) – that can be used to assess a child’s level of functioning at approximately one year of age. Among normal healthy infants, both indices have a mean value of 100. As part of a study investigating the development and neurologic status of children who had 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 failure. 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 associated risk of brain injury.

Sample	N	Mean MDI scores	St. Dev
Low flow By-Pass Group	70	106.4	212.3594
Circulatory Arrest Group	73	103.0822	274.382

Assume that the MDI scores are approximately normally distributed in each group.

At the 5% significance level, test the null hypothesis that the mean MDI score at one year of age for the circulatory arrest treatment group is equal to the mean MDI score for the low-flow group. Also provide and interpret the corresponding 95% confidence interval.

Define the parameter(s) of interest.
State the null and alternative hypotheses.
State the significance level.
State what type of test you will perform, why you chose to use that test, and provide a check for any necessary assumptions.
State your test statistic and its null distribution.
Compute the test statistic BY HAND. Make a decision to reject or fail to reject based on either a p-value or by comparing the test statistic to a critical value (you can choose whichever you prefer).
State your conclusion in the context of the problem. Be sure to include the P-value and confidence interval.

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