The purpose of a study by Tahmassebi and Curzon (A-33) was to compare the mean salivary flow rate among subjects with cerebral palsy and among subjects in a control group. Each group had 10 subjects. The following table gives the mean flow rate in ml/minute as well as the standard error.

Group Sample Size Mean ml/minute Standard Error Cerebral palsy 10 0.220 0.0582 Control 10 0.334 0.1641 Source: J. F. Tahmassebi and M. E. J. Curzon, “The Cause of Drooling in Children with Cerebral Palsy—Hypersalivation or Swallowing Defect?” International Journal of Paediatric Dentistry, 13 (2003), 106–111.
Construct the 90 percent confidence interval for the difference in mean salivary flow rate for the two populations of subjects represented by the sample data. State the assumptions necessary for this to be a valid confidence interval.