How Many Classrooms

A district surveys students by choosing whole classrooms at random and measuring every student in each chosen room. Every classroom has exactly 16 students. Scores have a common variance $\sigma^2$, any two students in the same classroom have correlation $\rho = 0.2$, and students in different classrooms are independent. How many classrooms must be sampled so that the variance of the overall sample mean equals that of a simple random sample of 600 students drawn independently from the whole population?

• variance

Source: Design effect for one-stage cluster sampling, standard in Kish, Survey Sampling, and Cochran, Sampling Techniques. Statement written for AxiomIQ.