To estimate the population total Y = Σi=1N yi, where y1, y2, ..., yN are study variables and N is the size of the finite population, a sample of size n is drawn using PPSWR (p1, p2, ..., pN) scheme. If ŶHH is the Hansen-Hurwitz estimator for Y, then which of the following statements is correct?

Consider a finite population of size N = 100. Let T1 be the sample mean of a study variable based on a sample of size n (1 < n < N) under simple random sampling with replacement (SRSWR). Let T2 be the sample mean under simple random sampling without replacement (SRSWOR). If Var(T1) = 9 Var(T2), then the sample size n equals:

Stratified sampling is most effective when certain variance criteria are fulfilled. Which of the following conditions is INCORRECT regarding optimal stratification?