For Exercises 29–49, assume normality and use Welch's test and interval unless otherwise indicated.

Question 10.84

33. Children per Classroom. According to LocalSchoolDirectory.com, the sample mean number of children per teacher in the towns of Cupertino, California, and Santa Rosa, California, are 20.9 and 19.3, respectively. Suppose random samples of classrooms are taken from each county, with the following sample statistics.

Cupertino
Santa Rosa
  1. Construct and interpret a 99% confidence interval for .
  2. Use the confidence interval in (a) to test, at level of significance , whether differs from .

10.2.33

(a) (–1.047, 4.247). We are 99% confident that the interval captures the difference in the population mean number of children per teacher in the towns of Cupertino, California, and Santa Rosa, California.

(b) . lies inside of the interval (–1.047, 4.247), so we do not reject . There is insufficient evidence at the level of significance that the population mean number of children per teacher in the town of Cupertino, California, differs from the population mean number of children per teacher in the town of Santa Rosa, California.