Question

For all hypothesis tests, be sure to include information for all 7 steps. For any two-sample or paired t-tests that you perform, in Step 6, show the decision rule based on BOTH the critical value and the p-value. Use the online app for the t-distribution to compute your p-values.

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. 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” (n₁ = 73) and “low-flow bypass” (n₂ = 70).

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.

Here we focus on the MDI score only. The data for this study are on MDI scores is given in the table below:

Group	Sample Size	Mean MDI	St. Dev MDI
Circulatory Arrest	73	103.08	16.56
Low-Flow Bypass	70	106.40	14.57

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.

Answer 1