State whether the following statements are true or false and also give

Question

State whether the following statements are true or false and also give the reason in support of your answer: $(2 \times 5 = 10)$
a) In Two-Stage Sampling if $N = n$ , it becomes the Cluster Sampling.
b) Among all the members of the General Class of the estimators only Product estimator is an unbiased estimator of the Population mean.
c) With the following parameters $b = 10, k = 5, v = 10, r = 5$ , an Incomplete Block Design is found to be a Balanced Incomplete Block Design.
d) a 2³ Factorial design is One-half fractional factorial design of a 2⁶ full factorial design.
e) If M_i and $\bar{Y}_{i.}$ are correlated, the Cluster estimator $\bar{\bar{y}}_{n.}$ becomes an unbiased estimator of the Population Mean.

25 Mar 2026

Answer :

Word Count : 280

a) True. In two-stage sampling, if all the secondary units within each selected primary unit are observed (i.e., complete enumeration within selected clusters), the design reduces to cluster sampling because each selected primary unit is treated as a cluster and all its elements are included. b) False. The product estimator of the population mean is generally ______ _________ _____ ____ _______.
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