Worksheet 05: Introduction to Cluster Sampling

Worksheet
Published

April 12, 2023

A student wants to estimate the average GPA in their dorm. Obtaining a listing of all students in the hall and conducting an SRS would take a lot of time. Instead, since each of the 100 suites in the hall have 4 students, the student randomly samples 5 suites and collects GPA data for each student in the suite. A summary table is shown below.

person Suite 1 Suite 2 Suite 3 Suite 4 Suite 5
1 3.08 2.36 2.00 3.00 2.68
2 2.60 3.04 2.56 2.88 1.92
3 3.44 3.28 2.52 3.44 3.28
4 3.04 2.68 1.88 3.64 3.20

Using hand written equations, estimate the average GPA for all students living in that dorm, with a proper 95% CI. Interpret your interval